MinT - Best Known (40−37, 40, s)-Nets in Base 256

Best Known (40−37, 40, s)-Nets in Base 256

(40−37, 40, 260)-Net over F₂₅₆ — Constructive and digital

Digital (3, 40, 260)-net over F₂₅₆, using

net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(40−37, 40, 321)-Net over F₂₅₆ — Digital

Digital (3, 40, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 40, 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]

(40−37, 40, 4882)-Net in Base 256 — Upper bound on s

There is no (3, 40, 4883)-net in base 256, because

1 times m-reduction [i] would yield (3, 39, 4883)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 8345 406285 023125 650566 967157 750312 890587 137943 079816 846920 125839 951177 513348 853945 888526 491921 > 256³⁹ [i]