MinT - Best Known (45−39, 45, s)-Nets in Base 256

Best Known (45−39, 45, s)-Nets in Base 256

(45−39, 45, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 45, 263)-net over F₂₅₆, using

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

(45−39, 45, 321)-Net over F₂₅₆ — Digital

Digital (6, 45, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 45, 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]

(45−39, 45, 11730)-Net in Base 256 — Upper bound on s

There is no (6, 45, 11731)-net in base 256, because

1 times m-reduction [i] would yield (6, 44, 11731)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 9181 509331 777666 901454 772270 472621 640379 706912 539539 526099 419033 707950 739108 020581 707241 801283 779750 460096 > 256⁴⁴ [i]