MinT - Best Known (124−59, 124, s)-Nets in Base 16

Best Known (124−59, 124, s)-Nets in Base 16

(124−59, 124, 520)-Net over F₁₆ — Constructive and digital

Digital (65, 124, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 62, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(124−59, 124, 642)-Net over F₁₆ — Digital

Digital (65, 124, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (65, 126, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 63, 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]

(124−59, 124, 99561)-Net in Base 16 — Upper bound on s

There is no (65, 124, 99562)-net in base 16, because

1 times m-reduction [i] would yield (65, 123, 99562)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12789 034526 796657 715669 705618 089533 466507 846901 821240 533112 779174 162213 733641 605396 387715 499852 867059 460477 184533 895978 938173 759585 639212 243134 401896 > 16¹²³ [i]