MinT - Best Known (59, 110, s)-Nets in Base 16

Best Known (59, 110, s)-Nets in Base 16

(59, 110, 522)-Net over F₁₆ — Constructive and digital

Digital (59, 110, 522)-net over F₁₆, using

trace code for nets [i] based on digital (4, 55, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(59, 110, 642)-Net over F₁₆ — Digital

Digital (59, 110, 642)-net over F₁₆, using

4 times m-reduction [i] based on digital (59, 114, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 57, 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]

(59, 110, 120628)-Net in Base 16 — Upper bound on s

There is no (59, 110, 120629)-net in base 16, because

1 times m-reduction [i] would yield (59, 109, 120629)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177483 901724 231130 043948 551663 432115 469915 231529 689479 542167 720039 972521 548415 652490 763618 507249 350917 456101 060587 860987 889227 223376 > 16¹⁰⁹ [i]