diff --git a/.github/workflows/build.yaml b/.github/workflows/build.yaml
index 7785b1c..7319174 100644
--- a/.github/workflows/build.yaml
+++ b/.github/workflows/build.yaml
@@ -98,7 +98,7 @@ jobs:
       matrix:
         include: ${{ fromJSON(needs.matrix_config.outputs.MATRIX) }}
 
-    name: Build ${{ matrix.os_name }} ${{ matrix.target_arch }}
+    name: Build ${{ matrix.os_name }} ${{ matrix.target_arch }} ${{ matrix.container }}
     runs-on: ${{ matrix.os }}
     container:
       image: ${{ matrix.container }}
@@ -125,7 +125,7 @@ jobs:
       # actions.
       # See https://github.com/actions/runner/issues/801#issuecomment-2394425757
       - name: Patch native Alpine NodeJS into Runner environment
-        if: runner.os == 'Linux'
+        if: startsWith(matrix.container, 'alpine')
         run: |
           apk add nodejs
           sed -i "s:^ID=alpine:ID=NotpineForGHA:" /etc/os-release
@@ -140,10 +140,16 @@ jobs:
         shell: sh  # No bash in Alpine by default
 
       - name: Install Alpine Linux deps
-        if: runner.os == 'Linux'
+        if: startsWith(matrix.container, 'alpine')
         run: apk add bash npm sudo
         shell: sh  # No bash in Alpine until after this command
 
+      - name: Install Ubuntu Linux deps
+        if: startsWith(matrix.container, 'ubuntu')
+        # Sudo is needed by the first build script, but isn't in the default
+        # container image for Ubuntu.
+        run: apt -y update && apt -y upgrade && apt -y install sudo
+
       - uses: actions/checkout@v4
         with:
           path: repo-src
diff --git a/build-matrix.json b/build-matrix.json
index 2e4ba88..4375423 100644
--- a/build-matrix.json
+++ b/build-matrix.json
@@ -2,12 +2,29 @@
   "comment1": "runners hosted by GitHub, always enabled",
   "hosted": [
     {
+      "comment": "Alpine container for static Linux binaries",
       "os": "ubuntu-latest",
       "container": "alpine:3.20",
       "os_name": "linux",
       "target_arch": "x64",
       "exe_ext": ""
     },
+    {
+      "comment": "Ubuntu 24.04 with hardware acceleration",
+      "os": "ubuntu-latest",
+      "container": "ubuntu:24.04",
+      "os_name": "linux",
+      "target_arch": "x64",
+      "exe_ext": "-ubuntu-24.04"
+    },
+    {
+      "comment": "Ubuntu 22.04 with hardware acceleration",
+      "os": "ubuntu-latest",
+      "container": "ubuntu:22.04",
+      "os_name": "linux",
+      "target_arch": "x64",
+      "exe_ext": "-ubuntu-22.04"
+    },
     {
       "comment": "Explicit macOS version 13 is required for explicit x64 CPU.",
       "os": "macos-13",
@@ -16,7 +33,7 @@
       "exe_ext": ""
     },
     {
-      "comment": "Latest macOS version 13 is arm64 CPU.",
+      "comment": "Latest macOS version is arm64 CPU.",
       "os": "macos-latest",
       "os_name": "osx",
       "target_arch": "arm64",
@@ -33,11 +50,28 @@
   "comment2": "runners hosted by the owner, enabled by the ENABLE_SELF_HOSTED variable being set on the repo",
   "selfHosted": [
     {
+      "comment": "Alpine container for static Linux binaries",
       "os": "self-hosted-linux-arm64",
-      "container": "arm64v8/alpine:3.20",
+      "container": "alpine:3.20",
       "os_name": "linux",
       "target_arch": "arm64",
       "exe_ext": ""
+    },
+    {
+      "comment": "Ubuntu 24.04 with hardware acceleration",
+      "os": "self-hosted-linux-arm64",
+      "container": "ubuntu:24.04",
+      "os_name": "linux",
+      "target_arch": "arm64",
+      "exe_ext": "-ubuntu-24.04"
+    },
+    {
+      "comment": "Ubuntu 22.04 with hardware acceleration",
+      "os": "self-hosted-linux-arm64",
+      "container": "ubuntu:22.04",
+      "os_name": "linux",
+      "target_arch": "arm64",
+      "exe_ext": "-ubuntu-22.04"
     }
   ]
 }
diff --git a/build-scripts/00-packages.sh b/build-scripts/00-packages.sh
index bbe5ef2..dbf6e4a 100755
--- a/build-scripts/00-packages.sh
+++ b/build-scripts/00-packages.sh
@@ -46,12 +46,13 @@ if [[ "$RUNNER_OS" == "Linux" ]]; then
     sudo apt -y update
     sudo apt -y upgrade
     sudo apt -y install \
+      clang \
       cmake \
       curl \
       g++ \
       git \
       libffmpeg-nvenc-dev \
-      libvdpau-dev \
+      libva-dev \
       make \
       nasm \
       npm \
diff --git a/build-scripts/90-ffmpeg.sh b/build-scripts/90-ffmpeg.sh
index 056c2d8..c8aaf71 100755
--- a/build-scripts/90-ffmpeg.sh
+++ b/build-scripts/90-ffmpeg.sh
@@ -23,11 +23,27 @@ cd ffmpeg
 
 # Set some OS-specific environment variables and flags.
 if [[ "$RUNNER_OS" == "Linux" ]]; then
-  export CFLAGS="-static"
-  export LDFLAGS="-static"
+  if ../repo-src/is-alpine.sh; then
+    # Truly static builds are only possible in musl-based Alpine Linux.
+    # Go for a completely static binary, but this prevents the use of hardware
+    # acceleration.
+    export CFLAGS="-static"
+    export LDFLAGS="-static"
+  else
+    # We can't build a truly static binary, so we might as well enable hardware
+    # acceleration, which uses dynamic libraries and will depend heavily on the
+    # OS distribution.
+    PLATFORM_CONFIGURE_FLAGS="--enable-vaapi --enable-nvenc"
+    # TODO: Is AMF an option for us in this context?
 
-  # Enable platform-specific hardware acceleration.
-  PLATFORM_CONFIGURE_FLAGS="--enable-vdpau"
+    # This version of ffmpeg will accept NVEnc 11.5.1.3+, but not Ubuntu
+    # 22.04's packaged version, 11.5.1.1.  This patch makes it flexible enough
+    # to build with the older NVEnc version in Ubuntu Jammy.
+    # For code archaeologists, the commits that set the minimum beyond 11.5.1.1
+    # were https://github.com/ffmpeg/ffmpeg/commit/5c288a44 (released in n6.0)
+    # and https://github.com/ffmpeg/ffmpeg/commit/05f8b2ca (released in n6.1).
+    patch -p1 -i ../repo-src/ffmpeg-nvenc-jammy.patch
+  fi
 elif [[ "$RUNNER_OS" == "macOS" ]]; then
   export CFLAGS="-static"
   # You can't do a _truly_ static build on macOS except the kernel.
@@ -36,11 +52,10 @@ elif [[ "$RUNNER_OS" == "macOS" ]]; then
   # Enable platform-specific hardware acceleration.
   PLATFORM_CONFIGURE_FLAGS="--enable-videotoolbox"
 
-  # Disable x86 ASM on macOS.  It fails to build with an error about
-  # how macho64 format can't contain 32-bit assembly.  I'm not sure
-  # how else to resolve this, and from my searches, it appears that
-  # others are not having this problem with ffmpeg.  This is still a problem
-  # with n6.0.
+  # Disable x86 ASM on macOS.  It fails to build with an error about "32-bit
+  # absolute addressing is not supported in 64-bit mode".  I'm not sure how
+  # else to resolve this, and from my searches, it appears that others are not
+  # having this problem with ffmpeg.  This is still a problem with n7.1
   PLATFORM_CONFIGURE_FLAGS="$PLATFORM_CONFIGURE_FLAGS --disable-x86asm --disable-inline-asm"
 elif [[ "$RUNNER_OS" == "Windows" ]]; then
   # /usr/local/incude and /usr/local/lib are not in mingw's include
@@ -55,12 +70,6 @@ elif [[ "$RUNNER_OS" == "Windows" ]]; then
   PLATFORM_CONFIGURE_FLAGS="--target-os=mingw64"
 fi
 
-# Install a patch from https://github.com/FFmpeg/FFmpeg/commit/effadce6 to
-# resolve the binutils error "operand type mismatch for shr" on Windows,
-# described in https://github.com/msys2/MINGW-packages/issues/17946
-wget https://github.com/FFmpeg/FFmpeg/commit/effadce6.patch
-patch -p1 -i effadce6.patch
-
 if ! ./configure \
     --pkg-config-flags="--static" \
     --disable-ffplay \
diff --git a/build-scripts/99-check-static.sh b/build-scripts/99-check-static.sh
index 8bfae93..c27e53a 100755
--- a/build-scripts/99-check-static.sh
+++ b/build-scripts/99-check-static.sh
@@ -20,10 +20,16 @@ set -x
 cd ffmpeg
 
 if [[ "$RUNNER_OS" == "Linux" ]]; then
-  # If ldd succeeds, then these are dynamic executables, so we fail
-  # this step if ldd succeeds.  The output of ldd will still be logged.
-  ldd ffmpeg && exit 1
-  ldd ffprobe && exit 1
+  # We only check for static binaries on Alpine Linux.  In other distributions,
+  # these are not possible due to the use of glibc.  We allow glibc builds here
+  # because while tied to the distro, they at least give us the chance for
+  # hardware encoding.
+  if ../repo-src/is-alpine.sh; then
+    # If ldd succeeds, then these are dynamic executables, so we fail
+    # this step if ldd succeeds.  The output of ldd will still be logged.
+    ldd ffmpeg && exit 1
+    ldd ffprobe && exit 1
+  fi
 elif [[ "$RUNNER_OS" == "Windows" ]]; then
   # These will still be dynamic executables.
   # Capture the full list of DLL dependencies.
diff --git a/ffmpeg-nvenc-jammy.patch b/ffmpeg-nvenc-jammy.patch
new file mode 100644
index 0000000..af29d9f
--- /dev/null
+++ b/ffmpeg-nvenc-jammy.patch
@@ -0,0 +1,48 @@
+FFmpeg n7.1 will accept NVEnc 11.5.1.3+, but not Ubuntu 22.04's packaged
+version, 11.5.1.1.  This patch makes it flexible enough to build with the older
+NVEnc version in Ubuntu Jammy.  For code archaeologists, the commits that set
+the minimum beyond 11.5.1.1 were
+https://github.com/ffmpeg/ffmpeg/commit/5c288a44 (released in n6.0) and
+https://github.com/ffmpeg/ffmpeg/commit/05f8b2ca (released in n6.1).
+
+
+diff --git a/configure b/configure
+index d77a55b653..c28dcffbb0 100755
+--- a/configure
++++ b/configure
+@@ -6761,7 +6761,7 @@ if ! disabled ffnvcodec; then
+     ffnv_hdr_list="ffnvcodec/nvEncodeAPI.h ffnvcodec/dynlink_cuda.h ffnvcodec/dynlink_cuviddec.h ffnvcodec/dynlink_nvcuvid.h"
+     check_pkg_config ffnvcodec "ffnvcodec >= 12.1.14.0" "$ffnv_hdr_list" "" || \
+       check_pkg_config ffnvcodec "ffnvcodec >= 12.0.16.1 ffnvcodec < 12.1" "$ffnv_hdr_list" "" || \
+-      check_pkg_config ffnvcodec "ffnvcodec >= 11.1.5.3 ffnvcodec < 12.0" "$ffnv_hdr_list" "" || \
++      check_pkg_config ffnvcodec "ffnvcodec >= 11.1.5.1 ffnvcodec < 12.0" "$ffnv_hdr_list" "" || \
+       check_pkg_config ffnvcodec "ffnvcodec >= 11.0.10.3 ffnvcodec < 11.1" "$ffnv_hdr_list" "" || \
+       check_pkg_config ffnvcodec "ffnvcodec >= 8.1.24.15 ffnvcodec < 8.2" "$ffnv_hdr_list" ""
+ fi
+@@ -7388,7 +7388,7 @@ int main(void) { return 0; }
+ EOF
+ 
+ if enabled nvenc; then
+-    check_type "ffnvcodec/nvEncodeAPI.h" "NV_ENC_PIC_PARAMS_AV1"
++    check_type "ffnvcodec/nvEncodeAPI.h" "NV_ENC_PIC_PARAMS_AV1" || add_cflags -DJAMMY
+ fi
+ 
+ if enabled_any nvdec cuvid; then
+diff --git a/libavutil/hwcontext_cuda.c b/libavutil/hwcontext_cuda.c
+index 3de3847399..0815360a46 100644
+--- a/libavutil/hwcontext_cuda.c
++++ b/libavutil/hwcontext_cuda.c
+@@ -363,11 +363,13 @@ static int cuda_context_init(AVHWDeviceContext *device_ctx, int flags) {
+                                                     hwctx->internal->cuda_device));
+         if (ret < 0)
+             return ret;
++#ifndef JAMMY
+     } else if (flags & AV_CUDA_USE_CURRENT_CONTEXT) {
+         ret = CHECK_CU(cu->cuCtxGetCurrent(&hwctx->cuda_ctx));
+         if (ret < 0)
+             return ret;
+         av_log(device_ctx, AV_LOG_INFO, "Using current CUDA context.\n");
++#endif
+     } else {
+         ret = CHECK_CU(cu->cuCtxCreate(&hwctx->cuda_ctx, desired_flags,
+                                        hwctx->internal->cuda_device));
diff --git a/versions.txt b/versions.txt
index 1f4a823..37bd987 100644
--- a/versions.txt
+++ b/versions.txt
@@ -1,4 +1,4 @@
-ffmpeg: n6.0
+ffmpeg: n7.1
 libvpx: v1.13.0
 svt-av1: v1.7.0
 x264: a8b68ebf