Best Known (199, 236, s)-Nets in Base 3
(199, 236, 1494)-Net over F3 — Constructive and digital
Digital (199, 236, 1494)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- digital (175, 212, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 53, 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, 53, 370)-net over F81, using
- digital (6, 24, 14)-net over F3, using
(199, 236, 11078)-Net over F3 — Digital
Digital (199, 236, 11078)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 11078, F3, 37) (dual of [11078, 10842, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 19747, F3, 37) (dual of [19747, 19511, 38]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3233, 19744, F3, 37) (dual of [19744, 19511, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [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(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(316, 61, F3, 7) (dual of [61, 45, 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(28) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3233, 19744, F3, 37) (dual of [19744, 19511, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 19747, F3, 37) (dual of [19747, 19511, 38]-code), using
(199, 236, 6400028)-Net in Base 3 — Upper bound on s
There is no (199, 236, 6400029)-net in base 3, because
- 1 times m-reduction [i] would yield (199, 235, 6400029)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 13289 089634 797103 790944 292705 642492 809549 844303 409665 962081 274316 466485 105531 534544 063175 127696 883381 925687 791745 > 3235 [i]