MinT - Best Known (66−57, 66, s)-Nets in Base 256

Best Known (66−57, 66, s)-Nets in Base 256

(66−57, 66, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 66, 266)-net over F₂₅₆, using

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

(66−57, 66, 513)-Net over F₂₅₆ — Digital

Digital (9, 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]

(66−57, 66, 17245)-Net in Base 256 — Upper bound on s

There is no (9, 66, 17246)-net in base 256, because

1 times m-reduction [i] would yield (9, 65, 17246)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 434393 762509 125031 358521 405946 037166 892004 154402 456732 764105 149511 438450 240380 549560 434422 070596 699972 656494 939151 316120 470899 666025 619728 409333 995251 512641 > 256⁶⁵ [i]