MinT - Best Known (80−38, 80, s)-Nets in Base 16

Best Known (80−38, 80, s)-Nets in Base 16

(80−38, 80, 518)-Net over F₁₆ — Constructive and digital

Digital (42, 80, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 40, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(80−38, 80, 642)-Net over F₁₆ — Digital

Digital (42, 80, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 40, 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]

(80−38, 80, 62091)-Net in Base 16 — Upper bound on s

There is no (42, 80, 62092)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 136391 424477 494246 442661 415697 449265 420676 077040 055219 518231 257776 069938 677191 199224 373650 391896 > 16⁸⁰ [i]