Best Known (197−26, 197, s)-Nets in Base 3
(197−26, 197, 13629)-Net over F3 — Constructive and digital
Digital (171, 197, 13629)-net over F3, using
- 33 times duplication [i] based on digital (168, 194, 13629)-net over F3, using
- net defined by OOA [i] based on linear OOA(3194, 13629, F3, 26, 26) (dual of [(13629, 26), 354160, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3194, 177177, F3, 26) (dual of [177177, 176983, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3194, 177177, F3, 26) (dual of [177177, 176983, 27]-code), using
- net defined by OOA [i] based on linear OOA(3194, 13629, F3, 26, 26) (dual of [(13629, 26), 354160, 27]-NRT-code), using
(197−26, 197, 59063)-Net over F3 — Digital
Digital (171, 197, 59063)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3197, 59063, F3, 3, 26) (dual of [(59063, 3), 176992, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3194, 59062, F3, 3, 26) (dual of [(59062, 3), 176992, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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(25) ⊂ Ce(21) [i] based on
- OOA 3-folding [i] based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3194, 59062, F3, 3, 26) (dual of [(59062, 3), 176992, 27]-NRT-code), using
(197−26, 197, large)-Net in Base 3 — Upper bound on s
There is no (171, 197, large)-net in base 3, because
- 24 times m-reduction [i] would yield (171, 173, large)-net in base 3, but