MinT - Best Known (57−50, 57, s)-Nets in Base 256

Best Known (57−50, 57, s)-Nets in Base 256

(57−50, 57, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 57, 264)-net over F₂₅₆, using

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

(57−50, 57, 321)-Net over F₂₅₆ — Digital

Digital (7, 57, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 57, 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]

(57−50, 57, 12343)-Net in Base 256 — Upper bound on s

There is no (7, 57, 12344)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 186161 786363 147504 885626 766940 386474 886935 440586 792922 502822 926399 240192 347638 770157 637783 207189 651633 899254 667666 104218 158102 135908 289876 > 256⁵⁷ [i]