Best Known (72−18, 72, s)-Nets in Base 128
(72−18, 72, 932067)-Net over F128 — Constructive and digital
Digital (54, 72, 932067)-net over F128, using
- 1283 times duplication [i] based on digital (51, 69, 932067)-net over F128, using
- net defined by OOA [i] based on linear OOA(12869, 932067, F128, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12869, large, F128, 18) (dual of [large, large−69, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(12869, large, F128, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(12869, 932067, F128, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
(72−18, 72, 932326)-Net in Base 128 — Constructive
(54, 72, 932326)-net in base 128, using
- base change [i] based on digital (45, 63, 932326)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-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 (2, 11, 259)-net over F256, using
- (u, u+v)-construction [i] based on
(72−18, 72, large)-Net over F128 — Digital
Digital (54, 72, large)-net over F128, using
- 2 times m-reduction [i] based on digital (54, 74, large)-net over F128, using
(72−18, 72, large)-Net in Base 128 — Upper bound on s
There is no (54, 72, large)-net in base 128, because
- 16 times m-reduction [i] would yield (54, 56, large)-net in base 128, but