Best Known (29, 45, s)-Nets in Base 256
(29, 45, 8963)-Net over F256 — Constructive and digital
Digital (29, 45, 8963)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 771)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 257)-net over F256, using
- digital (0, 4, 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
- digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (15, 31, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 8192, F256, 16, 16) (dual of [(8192, 16), 131041, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- net defined by OOA [i] based on linear OOA(25631, 8192, F256, 16, 16) (dual of [(8192, 16), 131041, 17]-NRT-code), using
- digital (6, 14, 771)-net over F256, using
(29, 45, 422624)-Net over F256 — Digital
Digital (29, 45, 422624)-net over F256, using
(29, 45, large)-Net in Base 256 — Upper bound on s
There is no (29, 45, large)-net in base 256, because
- 14 times m-reduction [i] would yield (29, 31, large)-net in base 256, but