Best Known (94, 94+30, s)-Nets in Base 3
(94, 94+30, 400)-Net over F3 — Constructive and digital
Digital (94, 124, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 31, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(94, 94+30, 680)-Net over F3 — Digital
Digital (94, 124, 680)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3124, 680, F3, 30) (dual of [680, 556, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3124, 743, F3, 30) (dual of [743, 619, 31]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(3121, 730, F3, 31) (dual of [730, 609, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3109, 730, F3, 27) (dual of [730, 621, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3124, 743, F3, 30) (dual of [743, 619, 31]-code), using
(94, 94+30, 28230)-Net in Base 3 — Upper bound on s
There is no (94, 124, 28231)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 145609 130899 023563 947784 698585 414040 875218 432642 074367 404291 > 3124 [i]