MinT - Best Known (19−16, 19, s)-Nets in Base 256

Best Known (19−16, 19, s)-Nets in Base 256

(19−16, 19, 260)-Net over F₂₅₆ — Constructive and digital

Digital (3, 19, 260)-net over F₂₅₆, using

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

(19−16, 19, 321)-Net over F₂₅₆ — Digital

Digital (3, 19, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 19, 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]

(19−16, 19, 7736)-Net in Base 256 — Upper bound on s

There is no (3, 19, 7737)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 5714 351655 329648 454122 082769 848459 866365 302331 > 256¹⁹ [i]