MinT - Best Known (19, 19+17, s)-Nets in Base 16

Best Known (19, 19+17, s)-Nets in Base 16

(19, 19+17, 516)-Net over F₁₆ — Constructive and digital

Digital (19, 36, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 18, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(19, 19+17, 578)-Net over F₁₆ — Digital

Digital (19, 36, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 18, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(19, 19+17, 46514)-Net in Base 16 — Upper bound on s

There is no (19, 36, 46515)-net in base 16, because

1 times m-reduction [i] would yield (19, 35, 46515)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 393975 027423 450765 019061 043325 280782 548426 > 16³⁵ [i]