Best Known (28, 28+18, s)-Nets in Base 8
(28, 28+18, 256)-Net over F8 — Constructive and digital
Digital (28, 46, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 23, 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
(28, 28+18, 300)-Net in Base 8 — Constructive
(28, 46, 300)-net in base 8, using
- trace code for nets [i] based on (5, 23, 150)-net in base 64, using
- 5 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
- 5 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
(28, 28+18, 328)-Net over F8 — Digital
Digital (28, 46, 328)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(846, 328, F8, 18) (dual of [328, 282, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(846, 511, F8, 18) (dual of [511, 465, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(846, 511, F8, 18) (dual of [511, 465, 19]-code), using
(28, 28+18, 24454)-Net in Base 8 — Upper bound on s
There is no (28, 46, 24455)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 348556 348768 692847 513889 199900 102019 720288 > 846 [i]