Best Known (160, 196, s)-Nets in Base 3
(160, 196, 896)-Net over F3 — Constructive and digital
Digital (160, 196, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 49, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(160, 196, 3656)-Net over F3 — Digital
Digital (160, 196, 3656)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3196, 3656, F3, 36) (dual of [3656, 3460, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, 6575, F3, 36) (dual of [6575, 6379, 37]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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([0,18]) ⊂ C([0,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3196, 6575, F3, 36) (dual of [6575, 6379, 37]-code), using
(160, 196, 592117)-Net in Base 3 — Upper bound on s
There is no (160, 196, 592118)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3279 281349 465572 135820 556104 394543 391007 149637 695974 827709 122263 860330 063390 058215 212482 417325 > 3196 [i]