Best Known (5, 12, s)-Nets in Base 256
(5, 12, 771)-Net over F256 — Constructive and digital
Digital (5, 12, 771)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 771, F256, 7, 7) (dual of [(771, 7), 5385, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25612, 771, F256, 6, 7) (dual of [(771, 6), 4614, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(2562, 257, F256, 6, 2) (dual of [(257, 6), 1540, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1540,256) [i]
- linear OOA(2563, 257, F256, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1539,256) [i]
- linear OOA(2567, 257, F256, 6, 7) (dual of [(257, 6), 1535, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1535,256) [i]
- linear OOA(2562, 257, F256, 6, 2) (dual of [(257, 6), 1540, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(25612, 771, F256, 6, 7) (dual of [(771, 6), 4614, 8]-NRT-code), using
(5, 12, 1285)-Net over F256 — Digital
Digital (5, 12, 1285)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 1285, F256, 7, 7) (dual of [(1285, 7), 8983, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25612, 1285, F256, 6, 7) (dual of [(1285, 6), 7698, 8]-NRT-code), using
(5, 12, 4820107)-Net in Base 256 — Upper bound on s
There is no (5, 12, 4820108)-net in base 256, because
- 1 times m-reduction [i] would yield (5, 11, 4820108)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 309 485190 539342 463893 196571 > 25611 [i]