Best Known (151−18, 151, s)-Nets in Base 4
(151−18, 151, 466038)-Net over F4 — Constructive and digital
Digital (133, 151, 466038)-net over F4, using
- 42 times duplication [i] based on digital (131, 149, 466038)-net over F4, using
- net defined by OOA [i] based on linear OOA(4149, 466038, F4, 18, 18) (dual of [(466038, 18), 8388535, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4149, 4194342, F4, 18) (dual of [4194342, 4194193, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- OA 9-folding and stacking [i] based on linear OA(4149, 4194342, F4, 18) (dual of [4194342, 4194193, 19]-code), using
- net defined by OOA [i] based on linear OOA(4149, 466038, F4, 18, 18) (dual of [(466038, 18), 8388535, 19]-NRT-code), using
(151−18, 151, 2046942)-Net over F4 — Digital
Digital (133, 151, 2046942)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4151, 2046942, F4, 2, 18) (dual of [(2046942, 2), 4093733, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4151, 2097173, F4, 2, 18) (dual of [(2097173, 2), 4194195, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4151, 4194346, F4, 18) (dual of [4194346, 4194195, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4151, 4194347, F4, 18) (dual of [4194347, 4194196, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4151, 4194347, F4, 18) (dual of [4194347, 4194196, 19]-code), using
- OOA 2-folding [i] based on linear OA(4151, 4194346, F4, 18) (dual of [4194346, 4194195, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(4151, 2097173, F4, 2, 18) (dual of [(2097173, 2), 4194195, 19]-NRT-code), using
(151−18, 151, large)-Net in Base 4 — Upper bound on s
There is no (133, 151, large)-net in base 4, because
- 16 times m-reduction [i] would yield (133, 135, large)-net in base 4, but