Best Known (45−38, 45, s)-Nets in Base 128
(45−38, 45, 216)-Net over F128 — Constructive and digital
Digital (7, 45, 216)-net over F128, using
- t-expansion [i] based on digital (5, 45, 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
(45−38, 45, 258)-Net in Base 128 — Constructive
(7, 45, 258)-net in base 128, using
- 3 times m-reduction [i] based on (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
(45−38, 45, 262)-Net over F128 — Digital
Digital (7, 45, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(45−38, 45, 289)-Net in Base 128
(7, 45, 289)-net in base 128, using
- 3 times m-reduction [i] based on (7, 48, 289)-net in base 128, using
- base change [i] based on digital (1, 42, 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
- base change [i] based on digital (1, 42, 289)-net over F256, using
(45−38, 45, 6102)-Net in Base 128 — Upper bound on s
There is no (7, 45, 6103)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 66812 543578 943370 218481 004999 102215 227748 540684 739888 609170 643125 778836 626311 750553 145550 102508 > 12845 [i]