MinT - Best Known (57−51, 57, s)-Nets in Base 256

Best Known (57−51, 57, s)-Nets in Base 256

(57−51, 57, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 57, 263)-net over F₂₅₆, using

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

(57−51, 57, 321)-Net over F₂₅₆ — Digital

Digital (6, 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]

(57−51, 57, 9885)-Net in Base 256 — Upper bound on s

There is no (6, 57, 9886)-net in base 256, because

1 times m-reduction [i] would yield (6, 56, 9886)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 727 192846 276881 798840 278983 401418 428928 464302 917803 326687 985487 201484 386427 810305 493023 105407 033079 426735 255611 616714 480015 020011 712001 > 256⁵⁶ [i]