Best Known (199, 199+36, s)-Nets in Base 3
(199, 199+36, 1499)-Net over F3 — Constructive and digital
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
(199, 199+36, 12974)-Net over F3 — Digital
Digital (199, 235, 12974)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3235, 12974, F3, 36) (dual of [12974, 12739, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3235, 19755, F3, 36) (dual of [19755, 19520, 37]-code), using
- 2 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
- 2 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(3235, 19755, F3, 36) (dual of [19755, 19520, 37]-code), using
(199, 199+36, 6400028)-Net in Base 3 — Upper bound on s
There is no (199, 235, 6400029)-net in base 3, because
- 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]