MinT - Best Known (4, 4+37, s)-Nets in Base 256

Best Known (4, 4+37, s)-Nets in Base 256

(4, 4+37, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 41, 261)-net over F₂₅₆, using

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

(4, 4+37, 321)-Net over F₂₅₆ — Digital

Digital (4, 41, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 41, 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+37, 6647)-Net in Base 256 — Upper bound on s

There is no (4, 41, 6648)-net in base 256, because

1 times m-reduction [i] would yield (4, 40, 6648)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 137418 177852 921047 962566 506582 312597 301801 500949 787610 064401 216082 165384 134110 350927 181739 408771 > 256⁴⁰ [i]