Best Known (236−36, 236, s)-Nets in Base 3
(236−36, 236, 1499)-Net over F3 — Constructive and digital
Digital (200, 236, 1499)-net over F3, using
- 31 times duplication [i] based on digital (199, 235, 1499)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (9, 27, 19)-net over F3, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- digital (172, 208, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 52, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 52, 370)-net over F81, using
- digital (9, 27, 19)-net over F3, using
- (u, u+v)-construction [i] based on
(236−36, 236, 13401)-Net over F3 — Digital
Digital (200, 236, 13401)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 13401, F3, 36) (dual of [13401, 13165, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 19756, F3, 36) (dual of [19756, 19520, 37]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3233, 19753, F3, 36) (dual of [19753, 19520, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(27) [i] based on
- linear OA(3217, 19683, F3, 37) (dual of [19683, 19466, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(316, 70, F3, 7) (dual of [70, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(36) ⊂ Ce(27) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3233, 19753, F3, 36) (dual of [19753, 19520, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 19756, F3, 36) (dual of [19756, 19520, 37]-code), using
(236−36, 236, 6802816)-Net in Base 3 — Upper bound on s
There is no (200, 236, 6802817)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 39867 334611 365206 040527 879599 133041 453983 820247 135818 459653 966177 713133 168268 958342 743701 065480 029081 314789 230665 > 3236 [i]