Best Known (8, 49, s)-Nets in Base 128
(8, 49, 216)-Net over F128 — Constructive and digital
Digital (8, 49, 216)-net over F128, using
- t-expansion [i] based on digital (5, 49, 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
(8, 49, 258)-Net in Base 128 — Constructive
(8, 49, 258)-net in base 128, using
- 7 times m-reduction [i] based on (8, 56, 258)-net in base 128, using
- base change [i] based on digital (1, 49, 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, 49, 258)-net over F256, using
(8, 49, 276)-Net over F128 — Digital
Digital (8, 49, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(8, 49, 289)-Net in Base 128
(8, 49, 289)-net in base 128, using
- 7 times m-reduction [i] based on (8, 56, 289)-net in base 128, using
- base change [i] based on digital (1, 49, 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, 49, 289)-net over F256, using
(8, 49, 7451)-Net in Base 128 — Upper bound on s
There is no (8, 49, 7452)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 48, 7452)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 140169 382474 648716 389907 050991 371451 653482 546167 318212 750573 258486 974450 730629 087978 412726 246855 293246 > 12848 [i]