MinT - Best Known (60−28, 60, s)-Nets in Base 16

Best Known (60−28, 60, s)-Nets in Base 16

(60−28, 60, 518)-Net over F₁₆ — Constructive and digital

Digital (32, 60, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 30, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(60−28, 60, 642)-Net over F₁₆ — Digital

Digital (32, 60, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 30, 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]

(60−28, 60, 58321)-Net in Base 16 — Upper bound on s

There is no (32, 60, 58322)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 767249 432763 301019 246889 376479 185301 940436 047416 322466 495895 192034 324296 > 16⁶⁰ [i]