Best Known (26, 26+14, s)-Nets in Base 16
(26, 26+14, 585)-Net over F16 — Constructive and digital
Digital (26, 40, 585)-net over F16, using
- net defined by OOA [i] based on linear OOA(1640, 585, F16, 14, 14) (dual of [(585, 14), 8150, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(1640, 4095, F16, 14) (dual of [4095, 4055, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(1640, 4095, F16, 14) (dual of [4095, 4055, 15]-code), using
(26, 26+14, 594)-Net in Base 16 — Constructive
(26, 40, 594)-net in base 16, using
- (u, u+v)-construction [i] based on
- (5, 12, 80)-net in base 16, using
- base change [i] based on digital (1, 8, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 8, 80)-net over F64, using
- digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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
- trace code for nets [i] based on digital (0, 14, 257)-net over F256, using
- (5, 12, 80)-net in base 16, using
(26, 26+14, 2883)-Net over F16 — Digital
Digital (26, 40, 2883)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1640, 2883, F16, 14) (dual of [2883, 2843, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using
(26, 26+14, 1712032)-Net in Base 16 — Upper bound on s
There is no (26, 40, 1712033)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 461501 797527 012974 853623 944749 149326 049062 854816 > 1640 [i]