MinT - Best Known (36, 68, s)-Nets in Base 16

Best Known (36, 68, s)-Nets in Base 16

(36, 68, 518)-Net over F₁₆ — Constructive and digital

Digital (36, 68, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 34, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(36, 68, 642)-Net over F₁₆ — Digital

Digital (36, 68, 642)-net over F₁₆, using

trace code for nets [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]

(36, 68, 59414)-Net in Base 16 — Upper bound on s

There is no (36, 68, 59415)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7588 919649 477098 710504 708655 132727 763423 758926 157474 425164 633228 934806 845692 762101 > 16⁶⁸ [i]