Best Known (108, 125, s)-Nets in Base 4
(108, 125, 131074)-Net over F4 — Constructive and digital
Digital (108, 125, 131074)-net over F4, using
- 41 times duplication [i] based on digital (107, 124, 131074)-net over F4, using
- net defined by OOA [i] based on linear OOA(4124, 131074, F4, 17, 17) (dual of [(131074, 17), 2228134, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4124, 1048593, F4, 17) (dual of [1048593, 1048469, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4124, 1048597, F4, 17) (dual of [1048597, 1048473, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4124, 1048597, F4, 17) (dual of [1048597, 1048473, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4124, 1048593, F4, 17) (dual of [1048593, 1048469, 18]-code), using
- net defined by OOA [i] based on linear OOA(4124, 131074, F4, 17, 17) (dual of [(131074, 17), 2228134, 18]-NRT-code), using
(108, 125, 392511)-Net over F4 — Digital
Digital (108, 125, 392511)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4125, 392511, F4, 2, 17) (dual of [(392511, 2), 784897, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4125, 524300, F4, 2, 17) (dual of [(524300, 2), 1048475, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4125, 1048600, F4, 17) (dual of [1048600, 1048475, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(4125, 1048600, F4, 17) (dual of [1048600, 1048475, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(4125, 524300, F4, 2, 17) (dual of [(524300, 2), 1048475, 18]-NRT-code), using
(108, 125, large)-Net in Base 4 — Upper bound on s
There is no (108, 125, large)-net in base 4, because
- 15 times m-reduction [i] would yield (108, 110, large)-net in base 4, but