Best Known (233, 260, s)-Nets in Base 4
(233, 260, 645294)-Net over F4 — Constructive and digital
Digital (233, 260, 645294)-net over F4, using
- 41 times duplication [i] based on digital (232, 259, 645294)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (214, 241, 645277)-net over F4, using
- net defined by OOA [i] based on linear OOA(4241, 645277, F4, 27, 27) (dual of [(645277, 27), 17422238, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4241, 8388602, F4, 27) (dual of [8388602, 8388361, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4241, large, F4, 27) (dual of [large, large−241, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4241, large, F4, 27) (dual of [large, large−241, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4241, 8388602, F4, 27) (dual of [8388602, 8388361, 28]-code), using
- net defined by OOA [i] based on linear OOA(4241, 645277, F4, 27, 27) (dual of [(645277, 27), 17422238, 28]-NRT-code), using
- digital (5, 18, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(233, 260, 5859285)-Net over F4 — Digital
Digital (233, 260, 5859285)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4260, 5859285, F4, 27) (dual of [5859285, 5859025, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4260, large, F4, 27) (dual of [large, large−260, 28]-code), using
- 19 times code embedding in larger space [i] based on linear OA(4241, large, F4, 27) (dual of [large, large−241, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- 19 times code embedding in larger space [i] based on linear OA(4241, large, F4, 27) (dual of [large, large−241, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4260, large, F4, 27) (dual of [large, large−260, 28]-code), using
(233, 260, large)-Net in Base 4 — Upper bound on s
There is no (233, 260, large)-net in base 4, because
- 25 times m-reduction [i] would yield (233, 235, large)-net in base 4, but