Best Known (94, 94+19, s)-Nets in Base 4
(94, 94+19, 7282)-Net over F4 — Constructive and digital
Digital (94, 113, 7282)-net over F4, using
- net defined by OOA [i] based on linear OOA(4113, 7282, F4, 19, 19) (dual of [(7282, 19), 138245, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4113, 65539, F4, 19) (dual of [65539, 65426, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4113, 65544, F4, 19) (dual of [65544, 65431, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4113, 65544, F4, 19) (dual of [65544, 65431, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4113, 65539, F4, 19) (dual of [65539, 65426, 20]-code), using
(94, 94+19, 32772)-Net over F4 — Digital
Digital (94, 113, 32772)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4113, 32772, F4, 2, 19) (dual of [(32772, 2), 65431, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4113, 65544, F4, 19) (dual of [65544, 65431, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4113, 65544, F4, 19) (dual of [65544, 65431, 20]-code), using
(94, 94+19, large)-Net in Base 4 — Upper bound on s
There is no (94, 113, large)-net in base 4, because
- 17 times m-reduction [i] would yield (94, 96, large)-net in base 4, but