MinT - Best Known (63, 120, s)-Nets in Base 16

Best Known (63, 120, s)-Nets in Base 16

(63, 120, 520)-Net over F₁₆ — Constructive and digital

Digital (63, 120, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 60, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(63, 120, 642)-Net over F₁₆ — Digital

Digital (63, 120, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (63, 122, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 61, 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]

(63, 120, 98708)-Net in Base 16 — Upper bound on s

There is no (63, 120, 98709)-net in base 16, because

1 times m-reduction [i] would yield (63, 119, 98709)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195117 550264 007973 205763 451478 790120 440553 972519 258577 158845 469425 159630 000939 322069 715113 047932 612516 921615 501788 461323 311151 241791 400107 080656 > 16¹¹⁹ [i]