Best Known (95−23, 95, s)-Nets in Base 3
(95−23, 95, 328)-Net over F3 — Constructive and digital
Digital (72, 95, 328)-net over F3, using
- 1 times m-reduction [i] based on digital (72, 96, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 24, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 24, 82)-net over F81, using
(95−23, 95, 575)-Net over F3 — Digital
Digital (72, 95, 575)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(395, 575, F3, 23) (dual of [575, 480, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(395, 745, F3, 23) (dual of [745, 650, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(391, 729, F3, 23) (dual of [729, 638, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(379, 729, F3, 20) (dual of [729, 650, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(395, 745, F3, 23) (dual of [745, 650, 24]-code), using
(95−23, 95, 29312)-Net in Base 3 — Upper bound on s
There is no (72, 95, 29313)-net in base 3, because
- 1 times m-reduction [i] would yield (72, 94, 29313)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 707 209099 007138 964064 124734 860874 023726 529019 > 394 [i]