MinT - Best Known (7, 65, s)-Nets in Base 256

Best Known (7, 65, s)-Nets in Base 256

(7, 65, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 65, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(7, 65, 321)-Net over F₂₅₆ — Digital

Digital (7, 65, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 65, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(7, 65, 11424)-Net in Base 256 — Upper bound on s

There is no (7, 65, 11425)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 439551 709092 780658 929836 574194 516331 077710 929095 273582 340226 942530 943236 692645 234689 737875 663126 455973 887632 494973 843963 907800 226157 964582 191599 588633 785376 > 256⁶⁵ [i]