Best Known (145, 164, s)-Nets in Base 4
(145, 164, 466039)-Net over F4 — Constructive and digital
Digital (145, 164, 466039)-net over F4, using
- 41 times duplication [i] based on digital (144, 163, 466039)-net over F4, using
- net defined by OOA [i] based on linear OOA(4163, 466039, F4, 19, 19) (dual of [(466039, 19), 8854578, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4163, 4194352, F4, 19) (dual of [4194352, 4194189, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4163, 4194356, F4, 19) (dual of [4194356, 4194193, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4163, 4194356, F4, 19) (dual of [4194356, 4194193, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4163, 4194352, F4, 19) (dual of [4194352, 4194189, 20]-code), using
- net defined by OOA [i] based on linear OOA(4163, 466039, F4, 19, 19) (dual of [(466039, 19), 8854578, 20]-NRT-code), using
(145, 164, 2097178)-Net over F4 — Digital
Digital (145, 164, 2097178)-net over F4, using
- 41 times duplication [i] based on digital (144, 163, 2097178)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4163, 2097178, F4, 2, 19) (dual of [(2097178, 2), 4194193, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4163, 4194356, F4, 19) (dual of [4194356, 4194193, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(4163, 4194356, F4, 19) (dual of [4194356, 4194193, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4163, 2097178, F4, 2, 19) (dual of [(2097178, 2), 4194193, 20]-NRT-code), using
(145, 164, large)-Net in Base 4 — Upper bound on s
There is no (145, 164, large)-net in base 4, because
- 17 times m-reduction [i] would yield (145, 147, large)-net in base 4, but