Best Known (104−15, 104, s)-Nets in Base 16
(104−15, 104, 2397513)-Net over F16 — Constructive and digital
Digital (89, 104, 2397513)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (11, 18, 771)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 257)-net over F16, using
- net defined by OOA [i] based on linear OOA(164, 257, F16, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(164, 257, F16, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(164, 257, F16, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
- digital (7, 14, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- digital (1, 4, 257)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (71, 86, 2396742)-net over F16, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- digital (11, 18, 771)-net over F16, using
(104−15, 104, large)-Net over F16 — Digital
Digital (89, 104, large)-net over F16, using
- 5 times m-reduction [i] based on digital (89, 109, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
(104−15, 104, large)-Net in Base 16 — Upper bound on s
There is no (89, 104, large)-net in base 16, because
- 13 times m-reduction [i] would yield (89, 91, large)-net in base 16, but