MinT - Best Known (38−18, 38, s)-Nets in Base 16

Best Known (38−18, 38, s)-Nets in Base 16

(38−18, 38, 516)-Net over F₁₆ — Constructive and digital

Digital (20, 38, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 19, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(38−18, 38, 578)-Net over F₁₆ — Digital

Digital (20, 38, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 19, 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]

(38−18, 38, 33547)-Net in Base 16 — Upper bound on s

There is no (20, 38, 33548)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5709 444988 527757 286513 329295 313080 811694 567081 > 16³⁸ [i]