Best Known (28−20, 28, s)-Nets in Base 128
(28−20, 28, 216)-Net over F128 — Constructive and digital
Digital (8, 28, 216)-net over F128, using
- t-expansion [i] based on digital (5, 28, 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
(28−20, 28, 261)-Net in Base 128 — Constructive
(8, 28, 261)-net in base 128, using
- 4 times m-reduction [i] based on (8, 32, 261)-net in base 128, using
- base change [i] based on digital (4, 28, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 28, 261)-net over F256, using
(28−20, 28, 276)-Net over F128 — Digital
Digital (8, 28, 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
(28−20, 28, 321)-Net in Base 128
(8, 28, 321)-net in base 128, using
- 20 times m-reduction [i] based on (8, 48, 321)-net in base 128, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
(28−20, 28, 28332)-Net in Base 128 — Upper bound on s
There is no (8, 28, 28333)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 100438 808328 826299 629810 530167 887772 433489 054102 343462 510826 > 12828 [i]