MinT - Best Known (52−45, 52, s)-Nets in Base 256

Best Known (52−45, 52, s)-Nets in Base 256

(52−45, 52, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 52, 264)-net over F₂₅₆, using

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

(52−45, 52, 321)-Net over F₂₅₆ — Digital

Digital (7, 52, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 52, 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]

(52−45, 52, 13574)-Net in Base 256 — Upper bound on s

There is no (7, 52, 13575)-net in base 256, because

1 times m-reduction [i] would yield (7, 51, 13575)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 661 973727 120937 236880 401891 916951 762937 023941 761021 075645 476657 701641 043346 432529 536833 537669 522268 716323 021442 355231 611376 > 256⁵¹ [i]