Best Known (70−18, 70, s)-Nets in Base 128
(70−18, 70, 932067)-Net over F128 — Constructive and digital
Digital (52, 70, 932067)-net over F128, using
- 1281 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
(70−18, 70, 932217)-Net in Base 128 — Constructive
(52, 70, 932217)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- (42, 60, 932067)-net in base 128, using
- net defined by OOA [i] based on OOA(12860, 932067, S128, 18, 18), using
- OA 9-folding and stacking [i] based on OA(12860, large, S128, 18), using
- discarding parts of the base [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]
- discarding parts of the base [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- OA 9-folding and stacking [i] based on OA(12860, large, S128, 18), using
- net defined by OOA [i] based on OOA(12860, 932067, S128, 18, 18), using
- digital (1, 10, 150)-net over F128, using
(70−18, 70, large)-Net over F128 — Digital
Digital (52, 70, large)-net over F128, using
- t-expansion [i] based on digital (51, 70, large)-net over F128, using
(70−18, 70, large)-Net in Base 128 — Upper bound on s
There is no (52, 70, large)-net in base 128, because
- 16 times m-reduction [i] would yield (52, 54, large)-net in base 128, but