Best Known (149, 149+26, s)-Nets in Base 3
(149, 149+26, 4544)-Net over F3 — Constructive and digital
Digital (149, 175, 4544)-net over F3, using
- net defined by OOA [i] based on linear OOA(3175, 4544, F3, 26, 26) (dual of [(4544, 26), 117969, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3175, 59072, F3, 26) (dual of [59072, 58897, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3175, 59073, F3, 26) (dual of [59073, 58898, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(34, 24, F3, 2) (dual of [24, 20, 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(3175, 59073, F3, 26) (dual of [59073, 58898, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3175, 59072, F3, 26) (dual of [59072, 58897, 27]-code), using
(149, 149+26, 19691)-Net over F3 — Digital
Digital (149, 175, 19691)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3175, 19691, F3, 3, 26) (dual of [(19691, 3), 58898, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3175, 59073, F3, 26) (dual of [59073, 58898, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(34, 24, F3, 2) (dual of [24, 20, 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
- OOA 3-folding [i] based on linear OA(3175, 59073, F3, 26) (dual of [59073, 58898, 27]-code), using
(149, 149+26, 7501732)-Net in Base 3 — Upper bound on s
There is no (149, 175, 7501733)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 313487 241891 742008 976579 947888 518183 039597 418580 172195 470297 794540 598520 591657 605691 > 3175 [i]