MinT - Best Known (54, 101, s)-Nets in Base 16

Best Known (54, 101, s)-Nets in Base 16

(54, 101, 520)-Net over F₁₆ — Constructive and digital

Digital (54, 101, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (54, 102, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 51, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(54, 101, 642)-Net over F₁₆ — Digital

Digital (54, 101, 642)-net over F₁₆, using

3 times m-reduction [i] based on digital (54, 104, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 52, 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]

(54, 101, 108048)-Net in Base 16 — Upper bound on s

There is no (54, 101, 108049)-net in base 16, because

1 times m-reduction [i] would yield (54, 100, 108049)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 582500 328653 146750 446896 901847 291587 228266 602365 673797 614120 804978 845353 441997 669414 696357 113719 516458 860216 190959 750656 > 16¹⁰⁰ [i]