MinT - Best Known (64−30, 64, s)-Nets in Base 16

Best Known (64−30, 64, s)-Nets in Base 16

(64−30, 64, 518)-Net over F₁₆ — Constructive and digital

Digital (34, 64, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 32, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(64−30, 64, 642)-Net over F₁₆ — Digital

Digital (34, 64, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 32, 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]

(64−30, 64, 58775)-Net in Base 16 — Upper bound on s

There is no (34, 64, 58776)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 115812 720205 258939 345426 295699 217667 577590 930510 459603 445338 141555 418660 230726 > 16⁶⁴ [i]