Best Known (203−19, 203, s)-Nets in Base 4
(203−19, 203, 932580)-Net over F4 — Constructive and digital
Digital (184, 203, 932580)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (25, 34, 514)-net over F4, using
- trace code for nets [i] based on digital (8, 17, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(8,256) in PG(16,16)) for nets [i] based on digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base reduction for projective spaces (embedding PG(8,256) in PG(16,16)) for nets [i] based on digital (0, 9, 257)-net over F256, using
- trace code for nets [i] based on digital (8, 17, 257)-net over F16, using
- digital (150, 169, 932066)-net over F4, using
- net defined by OOA [i] based on linear OOA(4169, 932066, F4, 19, 19) (dual of [(932066, 19), 17709085, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4169, 8388595, F4, 19) (dual of [8388595, 8388426, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4169, 8388595, F4, 19) (dual of [8388595, 8388426, 20]-code), using
- net defined by OOA [i] based on linear OOA(4169, 932066, F4, 19, 19) (dual of [(932066, 19), 17709085, 20]-NRT-code), using
- digital (25, 34, 514)-net over F4, using
(203−19, 203, large)-Net over F4 — Digital
Digital (184, 203, large)-net over F4, using
- 46 times duplication [i] based on digital (178, 197, large)-net over F4, using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
(203−19, 203, large)-Net in Base 4 — Upper bound on s
There is no (184, 203, large)-net in base 4, because
- 17 times m-reduction [i] would yield (184, 186, large)-net in base 4, but