Best Known (236−45, 236, s)-Nets in Base 3
(236−45, 236, 896)-Net over F3 — Constructive and digital
Digital (191, 236, 896)-net over F3, using
- t-expansion [i] based on digital (190, 236, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 59, 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, 59, 224)-net over F81, using
(236−45, 236, 3280)-Net over F3 — Digital
Digital (191, 236, 3280)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 3280, F3, 45) (dual of [3280, 3044, 46]-code), using
- 1 times truncation [i] based on linear OA(3237, 3281, F3, 46) (dual of [3281, 3044, 47]-code), using
- an extension Ce(45) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 1 times truncation [i] based on linear OA(3237, 3281, F3, 46) (dual of [3281, 3044, 47]-code), using
(236−45, 236, 565365)-Net in Base 3 — Upper bound on s
There is no (191, 236, 565366)-net in base 3, because
- 1 times m-reduction [i] would yield (191, 235, 565366)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 13289 534309 645367 632440 819188 063628 555703 336397 895408 472504 612178 808010 742154 448894 416119 194472 737513 679830 080917 > 3235 [i]