MinT - Best Known (40, 73, s)-Nets in Base 16

Best Known (40, 73, s)-Nets in Base 16

(40, 73, 520)-Net over F₁₆ — Constructive and digital

Digital (40, 73, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (40, 74, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 37, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(40, 73, 642)-Net over F₁₆ — Digital

Digital (40, 73, 642)-net over F₁₆, using

3 times m-reduction [i] based on digital (40, 76, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 38, 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]

(40, 73, 118838)-Net in Base 16 — Upper bound on s

There is no (40, 73, 118839)-net in base 16, because

1 times m-reduction [i] would yield (40, 72, 118839)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 497 376485 699716 951141 322546 493570 514830 596696 988943 927288 480116 061813 006487 233054 187611 > 16⁷² [i]