Best Known (171, 171+28, s)-Nets in Base 3
(171, 171+28, 12653)-Net over F3 — Constructive and digital
Digital (171, 199, 12653)-net over F3, using
- net defined by OOA [i] based on linear OOA(3199, 12653, F3, 28, 28) (dual of [(12653, 28), 354085, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3199, 177142, F3, 28) (dual of [177142, 176943, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3199, 177142, F3, 28) (dual of [177142, 176943, 29]-code), using
(171, 171+28, 44286)-Net over F3 — Digital
Digital (171, 199, 44286)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 44286, F3, 4, 28) (dual of [(44286, 4), 176945, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3199, 177144, F3, 28) (dual of [177144, 176945, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- OOA 4-folding [i] based on linear OA(3199, 177144, F3, 28) (dual of [177144, 176945, 29]-code), using
(171, 171+28, large)-Net in Base 3 — Upper bound on s
There is no (171, 199, large)-net in base 3, because
- 26 times m-reduction [i] would yield (171, 173, large)-net in base 3, but