MinT - Best Known (31−26, 31, s)-Nets in Base 256

Best Known (31−26, 31, s)-Nets in Base 256

(31−26, 31, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 31, 262)-net over F₂₅₆, using

net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(31−26, 31, 321)-Net over F₂₅₆ — Digital

Digital (5, 31, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 31, 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]

(31−26, 31, 12285)-Net in Base 256 — Upper bound on s

There is no (5, 31, 12286)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 452 749878 591654 525669 307770 694107 063775 350786 136112 720269 135047 688998 440041 > 256³¹ [i]