MinT - Best Known (9, 9+47, s)-Nets in Base 256

Best Known (9, 9+47, s)-Nets in Base 256

(9, 9+47, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 56, 266)-net over F₂₅₆, using

net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(9, 9+47, 513)-Net over F₂₅₆ — Digital

Digital (9, 56, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 56, 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]

(9, 9+47, 21209)-Net in Base 256 — Upper bound on s

There is no (9, 56, 21210)-net in base 256, because

1 times m-reduction [i] would yield (9, 55, 21210)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 841751 580765 662615 561118 920264 742351 386390 107765 554167 697470 293904 417426 606714 361510 492622 075875 685544 094401 725255 752738 176092 598276 > 256⁵⁵ [i]