MinT - Best Known (21, 21+45, s)-Nets in Base 256

Best Known (21, 21+45, s)-Nets in Base 256

(21, 21+45, 278)-Net over F₂₅₆ — Constructive and digital

Digital (21, 66, 278)-net over F₂₅₆, using

net from sequence [i] based on digital (21, 277)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(21, 21+45, 513)-Net over F₂₅₆ — Digital

Digital (21, 66, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 66, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(21, 21+45, 462974)-Net in Base 256 — Upper bound on s

There is no (21, 66, 462975)-net in base 256, because

1 times m-reduction [i] would yield (21, 65, 462975)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 432430 338665 335253 282156 851471 315931 679135 094988 280825 359515 426590 529031 548436 347747 163315 732272 889544 258528 649041 551611 635363 500633 601179 974531 774581 684751 > 256⁶⁵ [i]