Best Known (246−46, 246, s)-Nets in Base 3
(246−46, 246, 896)-Net over F3 — Constructive and digital
Digital (200, 246, 896)-net over F3, using
- t-expansion [i] based on digital (199, 246, 896)-net over F3, using
- 2 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 62, 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, 62, 224)-net over F81, using
- 2 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
(246−46, 246, 3872)-Net over F3 — Digital
Digital (200, 246, 3872)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3246, 3872, F3, 46) (dual of [3872, 3626, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 6582, F3, 46) (dual of [6582, 6336, 47]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3245, 6581, F3, 46) (dual of [6581, 6336, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(42) [i] based on
- linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 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(45) ⊂ Ce(42) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3245, 6581, F3, 46) (dual of [6581, 6336, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 6582, F3, 46) (dual of [6582, 6336, 47]-code), using
(246−46, 246, 597768)-Net in Base 3 — Upper bound on s
There is no (200, 246, 597769)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2354 178465 158783 878186 416774 455851 871661 851187 896870 563846 707846 216977 269777 524504 499656 846296 518135 826460 184185 004395 > 3246 [i]