Best Known (94−13, 94, s)-Nets in Base 4
(94−13, 94, 174766)-Net over F4 — Constructive and digital
Digital (81, 94, 174766)-net over F4, using
- net defined by OOA [i] based on linear OOA(494, 174766, F4, 13, 13) (dual of [(174766, 13), 2271864, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(494, 1048597, F4, 13) (dual of [1048597, 1048503, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- OOA 6-folding and stacking with additional row [i] based on linear OA(494, 1048597, F4, 13) (dual of [1048597, 1048503, 14]-code), using
(94−13, 94, 522157)-Net over F4 — Digital
Digital (81, 94, 522157)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(494, 522157, F4, 2, 13) (dual of [(522157, 2), 1044220, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(494, 524298, F4, 2, 13) (dual of [(524298, 2), 1048502, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(494, 1048596, F4, 13) (dual of [1048596, 1048502, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(494, 1048597, F4, 13) (dual of [1048597, 1048503, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(494, 1048597, F4, 13) (dual of [1048597, 1048503, 14]-code), using
- OOA 2-folding [i] based on linear OA(494, 1048596, F4, 13) (dual of [1048596, 1048502, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(494, 524298, F4, 2, 13) (dual of [(524298, 2), 1048502, 14]-NRT-code), using
(94−13, 94, large)-Net in Base 4 — Upper bound on s
There is no (81, 94, large)-net in base 4, because
- 11 times m-reduction [i] would yield (81, 83, large)-net in base 4, but