Best Known (44, 44+18, s)-Nets in Base 256
(44, 44+18, 932325)-Net over F256 — Constructive and digital
Digital (44, 62, 932325)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- digital (1, 10, 258)-net over F256, using
(44, 44+18, large)-Net over F256 — Digital
Digital (44, 62, large)-net over F256, using
- 2561 times duplication [i] based on digital (43, 61, large)-net over F256, using
- t-expansion [i] based on digital (42, 61, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
- t-expansion [i] based on digital (42, 61, large)-net over F256, using
(44, 44+18, large)-Net in Base 256 — Upper bound on s
There is no (44, 62, large)-net in base 256, because
- 16 times m-reduction [i] would yield (44, 46, large)-net in base 256, but