Best Known (9, 9+44, s)-Nets in Base 128
(9, 9+44, 288)-Net over F128 — Constructive and digital
Digital (9, 53, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
(9, 9+44, 321)-Net in Base 128
(9, 53, 321)-net in base 128, using
- 3 times m-reduction [i] based on (9, 56, 321)-net in base 128, using
- base change [i] based on digital (2, 49, 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, 49, 321)-net over F256, using
(9, 9+44, 8491)-Net in Base 128 — Upper bound on s
There is no (9, 53, 8492)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 4820 955461 921468 383592 152705 492727 419233 553848 391734 757411 614739 288822 612025 522845 951995 413052 635862 528577 337508 > 12853 [i]