Best Known (36, 58, s)-Nets in Base 8
(36, 58, 354)-Net over F8 — Constructive and digital
Digital (36, 58, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 29, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(36, 58, 434)-Net over F8 — Digital
Digital (36, 58, 434)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(858, 434, F8, 22) (dual of [434, 376, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(858, 511, F8, 22) (dual of [511, 453, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(858, 511, F8, 22) (dual of [511, 453, 23]-code), using
(36, 58, 40512)-Net in Base 8 — Upper bound on s
There is no (36, 58, 40513)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 23946 164241 384984 624056 481370 190827 210538 773599 603264 > 858 [i]