Best Known (188, 216, s)-Nets in Base 3
(188, 216, 12663)-Net over F3 — Constructive and digital
Digital (188, 216, 12663)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- 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
- net defined by OOA [i] based on linear OOA(3199, 12653, F3, 28, 28) (dual of [(12653, 28), 354085, 29]-NRT-code), using
- digital (3, 17, 10)-net over F3, using
(188, 216, 61743)-Net over F3 — Digital
Digital (188, 216, 61743)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3216, 61743, F3, 2, 28) (dual of [(61743, 2), 123270, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3216, 88609, F3, 2, 28) (dual of [(88609, 2), 177002, 29]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3215, 88609, F3, 2, 28) (dual of [(88609, 2), 177003, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3215, 177218, F3, 28) (dual of [177218, 177003, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] 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]
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(316, 71, F3, 7) (dual of [71, 55, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3215, 177218, F3, 28) (dual of [177218, 177003, 29]-code), using
- 31 times duplication [i] based on linear OOA(3215, 88609, F3, 2, 28) (dual of [(88609, 2), 177003, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3216, 88609, F3, 2, 28) (dual of [(88609, 2), 177002, 29]-NRT-code), using
(188, 216, large)-Net in Base 3 — Upper bound on s
There is no (188, 216, large)-net in base 3, because
- 26 times m-reduction [i] would yield (188, 190, large)-net in base 3, but