Best Known (94, 94+18, s)-Nets in Base 4
(94, 94+18, 7286)-Net over F4 — Constructive and digital
Digital (94, 112, 7286)-net over F4, using
- net defined by OOA [i] based on linear OOA(4112, 7286, F4, 18, 18) (dual of [(7286, 18), 131036, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4112, 65574, F4, 18) (dual of [65574, 65462, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(4112, 65574, F4, 18) (dual of [65574, 65462, 19]-code), using
(94, 94+18, 34045)-Net over F4 — Digital
Digital (94, 112, 34045)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4112, 34045, F4, 18) (dual of [34045, 33933, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using
(94, 94+18, large)-Net in Base 4 — Upper bound on s
There is no (94, 112, large)-net in base 4, because
- 16 times m-reduction [i] would yield (94, 96, large)-net in base 4, but