MinT - Best Known (51−45, 51, s)-Nets in Base 256

Best Known (51−45, 51, s)-Nets in Base 256

(51−45, 51, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 51, 263)-net over F₂₅₆, using

net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(51−45, 51, 321)-Net over F₂₅₆ — Digital

Digital (6, 51, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 51, 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]

(51−45, 51, 10547)-Net in Base 256 — Upper bound on s

There is no (6, 51, 10548)-net in base 256, because

1 times m-reduction [i] would yield (6, 50, 10548)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 584893 047167 097831 378383 005132 731063 843106 453975 609056 261183 862373 403256 918768 934552 405654 444149 450711 753456 736351 790056 > 256⁵⁰ [i]