Best Known (91, 91+14, s)-Nets in Base 4
(91, 91+14, 149800)-Net over F4 — Constructive and digital
Digital (91, 105, 149800)-net over F4, using
- net defined by OOA [i] based on linear OOA(4105, 149800, F4, 14, 14) (dual of [(149800, 14), 2097095, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4105, 1048600, F4, 14) (dual of [1048600, 1048495, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(481, 1048576, F4, 11) (dual of [1048576, 1048495, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(44, 24, F4, 2) (dual of [24, 20, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OA 7-folding and stacking [i] based on linear OA(4105, 1048600, F4, 14) (dual of [1048600, 1048495, 15]-code), using
(91, 91+14, 524300)-Net over F4 — Digital
Digital (91, 105, 524300)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4105, 524300, F4, 2, 14) (dual of [(524300, 2), 1048495, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4105, 1048600, F4, 14) (dual of [1048600, 1048495, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(481, 1048576, F4, 11) (dual of [1048576, 1048495, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(44, 24, F4, 2) (dual of [24, 20, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(4105, 1048600, F4, 14) (dual of [1048600, 1048495, 15]-code), using
(91, 91+14, large)-Net in Base 4 — Upper bound on s
There is no (91, 105, large)-net in base 4, because
- 12 times m-reduction [i] would yield (91, 93, large)-net in base 4, but