Best Known (132, 145, s)-Nets in Base 4
(132, 145, 1419953)-Net over F4 — Constructive and digital
Digital (132, 145, 1419953)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (30, 36, 21853)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (27, 33, 21848)-net over F4, using
- net defined by OOA [i] based on linear OOA(433, 21848, F4, 6, 6) (dual of [(21848, 6), 131055, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(433, 65544, F4, 6) (dual of [65544, 65511, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(425, 65536, F4, 5) (dual of [65536, 65511, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(433, 65544, F4, 6) (dual of [65544, 65511, 7]-code), using
- net defined by OOA [i] based on linear OOA(433, 21848, F4, 6, 6) (dual of [(21848, 6), 131055, 7]-NRT-code), using
- digital (0, 3, 5)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (96, 109, 1398100)-net over F4, using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- digital (30, 36, 21853)-net over F4, using
(132, 145, large)-Net over F4 — Digital
Digital (132, 145, large)-net over F4, using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
(132, 145, large)-Net in Base 4 — Upper bound on s
There is no (132, 145, large)-net in base 4, because
- 11 times m-reduction [i] would yield (132, 134, large)-net in base 4, but