MinT - Best Known (45−40, 45, s)-Nets in Base 256

Best Known (45−40, 45, s)-Nets in Base 256

(45−40, 45, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 45, 262)-net over F₂₅₆, using

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

(45−40, 45, 321)-Net over F₂₅₆ — Digital

Digital (5, 45, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 45, 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]

(45−40, 45, 8527)-Net in Base 256 — Upper bound on s

There is no (5, 45, 8528)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 351641 142329 745412 332153 107706 165537 090003 618827 554959 402411 332552 719152 153940 612233 027310 664332 960631 380676 > 256⁴⁵ [i]