MinT - Best Known (45, 84, s)-Nets in Base 16

Best Known (45, 84, s)-Nets in Base 16

(45, 84, 520)-Net over F₁₆ — Constructive and digital

Digital (45, 84, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 42, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(45, 84, 642)-Net over F₁₆ — Digital

Digital (45, 84, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (45, 86, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 43, 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]

(45, 84, 96201)-Net in Base 16 — Upper bound on s

There is no (45, 84, 96202)-net in base 16, because

1 times m-reduction [i] would yield (45, 83, 96202)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8750 195508 782668 126934 103124 849305 177043 147071 093247 212231 983616 559083 009969 196346 114632 744548 864496 > 16⁸³ [i]