Best Known (51−20, 51, s)-Nets in Base 8
(51−20, 51, 256)-Net over F8 — Constructive and digital
Digital (31, 51, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (31, 52, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 26, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 26, 128)-net over F64, using
(51−20, 51, 300)-Net in Base 8 — Constructive
(31, 51, 300)-net in base 8, using
- 1 times m-reduction [i] based on (31, 52, 300)-net in base 8, using
- trace code for nets [i] based on (5, 26, 150)-net in base 64, using
- 2 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- 2 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
- trace code for nets [i] based on (5, 26, 150)-net in base 64, using
(51−20, 51, 311)-Net over F8 — Digital
Digital (31, 51, 311)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(851, 311, F8, 20) (dual of [311, 260, 21]-code), using
- 50 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0, 1, 16 times 0, 1, 27 times 0) [i] based on linear OA(848, 258, F8, 20) (dual of [258, 210, 21]-code), using
- trace code [i] based on linear OA(6424, 129, F64, 20) (dual of [129, 105, 21]-code), using
- extended algebraic-geometric code AGe(F,108P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6424, 129, F64, 20) (dual of [129, 105, 21]-code), using
- 50 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0, 1, 16 times 0, 1, 27 times 0) [i] based on linear OA(848, 258, F8, 20) (dual of [258, 210, 21]-code), using
(51−20, 51, 26093)-Net in Base 8 — Upper bound on s
There is no (31, 51, 26094)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 11418 537487 746375 524463 018140 691534 614231 842902 > 851 [i]