MinT - Best Known (45−41, 45, s)-Nets in Base 256

Best Known (45−41, 45, s)-Nets in Base 256

(45−41, 45, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 45, 261)-net over F₂₅₆, using

net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(45−41, 45, 321)-Net over F₂₅₆ — Digital

Digital (4, 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]

(45−41, 45, 6460)-Net in Base 256 — Upper bound on s

There is no (4, 45, 6461)-net in base 256, because

1 times m-reduction [i] would yield (4, 44, 6461)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 9194 698710 092855 731528 225607 513329 245616 814290 796864 664687 369745 142949 150073 302739 916197 978074 364519 813351 > 256⁴⁴ [i]