Best Known (3, 3+12, s)-Nets in Base 128
(3, 3+12, 192)-Net over F128 — Constructive and digital
Digital (3, 15, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
(3, 3+12, 258)-Net in Base 128 — Constructive
(3, 15, 258)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 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, 14, 258)-net over F256, using
(3, 3+12, 289)-Net in Base 128
(3, 15, 289)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 289)-net in base 128, using
- base change [i] based on digital (1, 14, 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, 14, 289)-net over F256, using
(3, 3+12, 4367)-Net in Base 128 — Upper bound on s
There is no (3, 15, 4368)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 40 616690 080051 751437 954544 162893 > 12815 [i]