Best Known (6, 6+34, s)-Nets in Base 128
(6, 6+34, 216)-Net over F128 — Constructive and digital
Digital (6, 40, 216)-net over F128, using
- t-expansion [i] based on digital (5, 40, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(6, 6+34, 243)-Net over F128 — Digital
Digital (6, 40, 243)-net over F128, using
- net from sequence [i] based on digital (6, 242)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 6 and N(F) ≥ 243, using
(6, 6+34, 258)-Net in Base 128 — Constructive
(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
(6, 6+34, 289)-Net in Base 128
(6, 40, 289)-net in base 128, using
- base change [i] based on digital (1, 35, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
(6, 6+34, 5123)-Net in Base 128 — Upper bound on s
There is no (6, 40, 5124)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 943822 724440 685303 235782 541218 656301 905541 726161 448907 281918 557241 893775 071178 092992 > 12840 [i]