Best Known (204, 236, s)-Nets in Base 3
(204, 236, 11073)-Net over F3 — Constructive and digital
Digital (204, 236, 11073)-net over F3, using
- net defined by OOA [i] based on linear OOA(3236, 11073, F3, 32, 32) (dual of [(11073, 32), 354100, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(3236, 177168, F3, 32) (dual of [177168, 176932, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 177173, F3, 32) (dual of [177173, 176937, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(3232, 177147, F3, 32) (dual of [177147, 176915, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3210, 177147, F3, 29) (dual of [177147, 176937, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 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(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 177173, F3, 32) (dual of [177173, 176937, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(3236, 177168, F3, 32) (dual of [177168, 176932, 33]-code), using
(204, 236, 52733)-Net over F3 — Digital
Digital (204, 236, 52733)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3236, 52733, F3, 3, 32) (dual of [(52733, 3), 157963, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 59057, F3, 3, 32) (dual of [(59057, 3), 176935, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3236, 177171, F3, 32) (dual of [177171, 176935, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 177173, F3, 32) (dual of [177173, 176937, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(3232, 177147, F3, 32) (dual of [177147, 176915, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3210, 177147, F3, 29) (dual of [177147, 176937, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 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(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 177173, F3, 32) (dual of [177173, 176937, 33]-code), using
- OOA 3-folding [i] based on linear OA(3236, 177171, F3, 32) (dual of [177171, 176935, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 59057, F3, 3, 32) (dual of [(59057, 3), 176935, 33]-NRT-code), using
(204, 236, large)-Net in Base 3 — Upper bound on s
There is no (204, 236, large)-net in base 3, because
- 30 times m-reduction [i] would yield (204, 206, large)-net in base 3, but