Best Known (64−45, 64, s)-Nets in Base 256
(64−45, 64, 276)-Net over F256 — Constructive and digital
Digital (19, 64, 276)-net over F256, using
- net from sequence [i] based on digital (19, 275)-sequence over F256, using
(64−45, 64, 513)-Net over F256 — Digital
Digital (19, 64, 513)-net over F256, using
- t-expansion [i] based on digital (8, 64, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
(64−45, 64, 279653)-Net in Base 256 — Upper bound on s
There is no (19, 64, 279654)-net in base 256, because
- 1 times m-reduction [i] would yield (19, 63, 279654)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 52 377146 515650 046617 190862 910886 017613 828150 828141 798610 470792 777556 307304 766038 348946 647721 065445 471268 471431 011690 881115 031398 806388 574899 308964 864816 > 25663 [i]