Best Known (201−26, 201, s)-Nets in Base 3
(201−26, 201, 13631)-Net over F3 — Constructive and digital
Digital (175, 201, 13631)-net over F3, using
- 31 times duplication [i] based on digital (174, 200, 13631)-net over F3, using
- net defined by OOA [i] based on linear OOA(3200, 13631, F3, 26, 26) (dual of [(13631, 26), 354206, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3200, 177203, F3, 26) (dual of [177203, 177003, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [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(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(312, 56, F3, 5) (dual of [56, 44, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(34, 28, F3, 2) (dual of [28, 24, 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
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- (u, u+v)-construction [i] based on
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3200, 177203, F3, 26) (dual of [177203, 177003, 27]-code), using
- net defined by OOA [i] based on linear OOA(3200, 13631, F3, 26, 26) (dual of [(13631, 26), 354206, 27]-NRT-code), using
(201−26, 201, 63301)-Net over F3 — Digital
Digital (175, 201, 63301)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 63301, F3, 2, 26) (dual of [(63301, 2), 126401, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3201, 88602, F3, 2, 26) (dual of [(88602, 2), 177003, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3199, 88601, F3, 2, 26) (dual of [(88601, 2), 177003, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [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(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(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3199, 88601, F3, 2, 26) (dual of [(88601, 2), 177003, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3201, 88602, F3, 2, 26) (dual of [(88602, 2), 177003, 27]-NRT-code), using
(201−26, 201, large)-Net in Base 3 — Upper bound on s
There is no (175, 201, large)-net in base 3, because
- 24 times m-reduction [i] would yield (175, 177, large)-net in base 3, but