Best Known (91, 91+13, s)-Nets in Base 4
(91, 91+13, 699054)-Net over F4 — Constructive and digital
Digital (91, 104, 699054)-net over F4, using
- 41 times duplication [i] based on digital (90, 103, 699054)-net over F4, using
- net defined by OOA [i] based on linear OOA(4103, 699054, F4, 13, 13) (dual of [(699054, 13), 9087599, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4103, 4194325, F4, 13) (dual of [4194325, 4194222, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, 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(4103, 4194325, F4, 13) (dual of [4194325, 4194222, 14]-code), using
- net defined by OOA [i] based on linear OOA(4103, 699054, F4, 13, 13) (dual of [(699054, 13), 9087599, 14]-NRT-code), using
(91, 91+13, 2088649)-Net over F4 — Digital
Digital (91, 104, 2088649)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4104, 2088649, F4, 2, 13) (dual of [(2088649, 2), 4177194, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4104, 2097165, F4, 2, 13) (dual of [(2097165, 2), 4194226, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4104, 4194330, F4, 13) (dual of [4194330, 4194226, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(44, 26, F4, 2) (dual of [26, 22, 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(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(4104, 4194330, F4, 13) (dual of [4194330, 4194226, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(4104, 2097165, F4, 2, 13) (dual of [(2097165, 2), 4194226, 14]-NRT-code), using
(91, 91+13, large)-Net in Base 4 — Upper bound on s
There is no (91, 104, large)-net in base 4, because
- 11 times m-reduction [i] would yield (91, 93, large)-net in base 4, but