Best Known (184−32, 184, s)-Nets in Base 3
(184−32, 184, 896)-Net over F3 — Constructive and digital
Digital (152, 184, 896)-net over F3, using
- t-expansion [i] based on digital (151, 184, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 46, 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
- trace code for nets [i] based on digital (13, 46, 224)-net over F81, using
(184−32, 184, 4871)-Net over F3 — Digital
Digital (152, 184, 4871)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3184, 4871, F3, 32) (dual of [4871, 4687, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3184, 6616, F3, 32) (dual of [6616, 6432, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3184, 6616, F3, 32) (dual of [6616, 6432, 33]-code), using
(184−32, 184, 1043269)-Net in Base 3 — Upper bound on s
There is no (152, 184, 1043270)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6170 368183 707562 019612 205871 234953 100390 371585 644570 974612 601826 522177 990561 827544 395425 > 3184 [i]