Best Known (225−31, 225, s)-Nets in Base 3
(225−31, 225, 11811)-Net over F3 — Constructive and digital
Digital (194, 225, 11811)-net over F3, using
- net defined by OOA [i] based on linear OOA(3225, 11811, F3, 31, 31) (dual of [(11811, 31), 365916, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3225, 177166, F3, 31) (dual of [177166, 176941, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 177173, F3, 31) (dual of [177173, 176948, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(34, 26, F3, 2) (dual of [26, 22, 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
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 177173, F3, 31) (dual of [177173, 176948, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3225, 177166, F3, 31) (dual of [177166, 176941, 32]-code), using
(225−31, 225, 45722)-Net over F3 — Digital
Digital (194, 225, 45722)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3225, 45722, F3, 3, 31) (dual of [(45722, 3), 136941, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3225, 59057, F3, 3, 31) (dual of [(59057, 3), 176946, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3225, 177171, F3, 31) (dual of [177171, 176946, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 177173, F3, 31) (dual of [177173, 176948, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(34, 26, F3, 2) (dual of [26, 22, 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
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 177173, F3, 31) (dual of [177173, 176948, 32]-code), using
- OOA 3-folding [i] based on linear OA(3225, 177171, F3, 31) (dual of [177171, 176946, 32]-code), using
- discarding factors / shortening the dual code based on linear OOA(3225, 59057, F3, 3, 31) (dual of [(59057, 3), 176946, 32]-NRT-code), using
(225−31, 225, large)-Net in Base 3 — Upper bound on s
There is no (194, 225, large)-net in base 3, because
- 29 times m-reduction [i] would yield (194, 196, large)-net in base 3, but