MinT - Best Known (3, 3+31, s)-Nets in Base 256

Best Known (3, 3+31, s)-Nets in Base 256

(3, 3+31, 260)-Net over F₂₅₆ — Constructive and digital

Digital (3, 34, 260)-net over F₂₅₆, using

net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(3, 3+31, 321)-Net over F₂₅₆ — Digital

Digital (3, 34, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 34, 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]

(3, 3+31, 4997)-Net in Base 256 — Upper bound on s

There is no (3, 34, 4998)-net in base 256, because

1 times m-reduction [i] would yield (3, 33, 4998)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 29 698762 358147 136069 166241 507266 366856 893820 080862 226733 944753 714466 409654 694976 > 256³³ [i]