Best Known (60−34, 60, s)-Nets in Base 128
(60−34, 60, 417)-Net over F128 — Constructive and digital
Digital (26, 60, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 17, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (9, 43, 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 (0, 17, 129)-net over F128, using
(60−34, 60, 515)-Net in Base 128 — Constructive
(26, 60, 515)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 20, 257)-net in base 128, using
- 4 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
- 4 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- (6, 40, 258)-net in base 128, using
- base change [i] based on digital (1, 35, 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, 35, 258)-net over F256, using
- (3, 20, 257)-net in base 128, using
(60−34, 60, 719)-Net over F128 — Digital
Digital (26, 60, 719)-net over F128, using
(60−34, 60, 1546503)-Net in Base 128 — Upper bound on s
There is no (26, 60, 1546504)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 2 707705 217149 555484 030734 097889 979227 516785 478315 496519 135102 753922 813712 447610 250452 861548 494078 525064 890400 832089 893867 026864 > 12860 [i]