Best Known (127, 151, s)-Nets in Base 3
(127, 151, 1643)-Net over F3 — Constructive and digital
Digital (127, 151, 1643)-net over F3, using
- net defined by OOA [i] based on linear OOA(3151, 1643, F3, 24, 24) (dual of [(1643, 24), 39281, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3151, 19716, F3, 24) (dual of [19716, 19565, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- OA 12-folding and stacking [i] based on linear OA(3151, 19716, F3, 24) (dual of [19716, 19565, 25]-code), using
(127, 151, 9858)-Net over F3 — Digital
Digital (127, 151, 9858)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3151, 9858, F3, 2, 24) (dual of [(9858, 2), 19565, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 19716, F3, 24) (dual of [19716, 19565, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3151, 19716, F3, 24) (dual of [19716, 19565, 25]-code), using
(127, 151, 2667505)-Net in Base 3 — Upper bound on s
There is no (127, 151, 2667506)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 109967 622998 777891 487609 893843 070222 674806 135540 063216 322574 504561 218169 > 3151 [i]