Best Known (156, 156+34, s)-Nets in Base 3
(156, 156+34, 896)-Net over F3 — Constructive and digital
Digital (156, 190, 896)-net over F3, using
- 32 times duplication [i] based on digital (154, 188, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 47, 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, 47, 224)-net over F81, using
(156, 156+34, 4175)-Net over F3 — Digital
Digital (156, 190, 4175)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3190, 4175, F3, 34) (dual of [4175, 3985, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3190, 6606, F3, 34) (dual of [6606, 6416, 35]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3188, 6604, F3, 34) (dual of [6604, 6416, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3188, 6604, F3, 34) (dual of [6604, 6416, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3190, 6606, F3, 34) (dual of [6606, 6416, 35]-code), using
(156, 156+34, 771680)-Net in Base 3 — Upper bound on s
There is no (156, 190, 771681)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4 498233 503534 683373 854402 624904 570836 154308 517695 538262 031598 240373 714141 145802 118329 947779 > 3190 [i]