Best Known (71−41, 71, s)-Nets in Base 128
(71−41, 71, 438)-Net over F128 — Constructive and digital
Digital (30, 71, 438)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 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
- digital (9, 50, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (1, 21, 150)-net over F128, using
(71−41, 71, 515)-Net in Base 128 — Constructive
(30, 71, 515)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 23, 257)-net in base 128, using
- 1 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 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
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 1 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- (7, 48, 258)-net in base 128, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- (3, 23, 257)-net in base 128, using
(71−41, 71, 703)-Net over F128 — Digital
Digital (30, 71, 703)-net over F128, using
(71−41, 71, 1551438)-Net in Base 128 — Upper bound on s
There is no (30, 71, 1551439)-net in base 128, because
- 1 times m-reduction [i] would yield (30, 70, 1551439)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 3196 671144 384206 926286 147280 679754 865728 715436 789979 708466 534197 577671 571804 591747 955848 758285 001201 911758 609612 533578 965505 666797 200579 605725 592644 > 12870 [i]