Best Known (166, 166+26, s)-Nets in Base 3
(166, 166+26, 13628)-Net over F3 — Constructive and digital
Digital (166, 192, 13628)-net over F3, using
- net defined by OOA [i] based on linear OOA(3192, 13628, F3, 26, 26) (dual of [(13628, 26), 354136, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3192, 177164, F3, 26) (dual of [177164, 176972, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3192, 177173, F3, 26) (dual of [177173, 176981, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3192, 177173, F3, 26) (dual of [177173, 176981, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3192, 177164, F3, 26) (dual of [177164, 176972, 27]-code), using
(166, 166+26, 56829)-Net over F3 — Digital
Digital (166, 192, 56829)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3192, 56829, F3, 3, 26) (dual of [(56829, 3), 170295, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3192, 59057, F3, 3, 26) (dual of [(59057, 3), 176979, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3192, 177171, F3, 26) (dual of [177171, 176979, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3192, 177173, F3, 26) (dual of [177173, 176981, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3192, 177173, F3, 26) (dual of [177173, 176981, 27]-code), using
- OOA 3-folding [i] based on linear OA(3192, 177171, F3, 26) (dual of [177171, 176979, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(3192, 59057, F3, 3, 26) (dual of [(59057, 3), 176979, 27]-NRT-code), using
(166, 166+26, large)-Net in Base 3 — Upper bound on s
There is no (166, 192, large)-net in base 3, because
- 24 times m-reduction [i] would yield (166, 168, large)-net in base 3, but