MinT - Best Known (4, 4+47, s)-Nets in Base 256

Best Known (4, 4+47, s)-Nets in Base 256

(4, 4+47, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 51, 261)-net over F₂₅₆, using

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

(4, 4+47, 321)-Net over F₂₅₆ — Digital

Digital (4, 51, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 51, 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]

(4, 4+47, 6345)-Net in Base 256 — Upper bound on s

There is no (4, 51, 6346)-net in base 256, because

1 times m-reduction [i] would yield (4, 50, 6346)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 587418 178926 990243 352373 031461 576706 823155 294255 190002 530905 379544 058791 581446 320387 364272 965927 620896 614334 731963 893616 > 256⁵⁰ [i]