Best Known (98−28, 98, s)-Nets in Base 7
(98−28, 98, 688)-Net over F7 — Constructive and digital
Digital (70, 98, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 49, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(98−28, 98, 2410)-Net over F7 — Digital
Digital (70, 98, 2410)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(798, 2410, F7, 28) (dual of [2410, 2312, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- linear OA(797, 2401, F7, 29) (dual of [2401, 2304, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(789, 2401, F7, 26) (dual of [2401, 2312, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
(98−28, 98, 829828)-Net in Base 7 — Upper bound on s
There is no (70, 98, 829829)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 66010 707361 132372 842196 612395 896340 482195 023987 928621 907279 177591 778555 682137 278553 > 798 [i]