MinT - Best Known (49, 49+43, s)-Nets in Base 16

Best Known (49, 49+43, s)-Nets in Base 16

(49, 49+43, 520)-Net over F₁₆ — Constructive and digital

Digital (49, 92, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 46, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(49, 49+43, 642)-Net over F₁₆ — Digital

Digital (49, 92, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (49, 94, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 47, 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]

(49, 49+43, 95543)-Net in Base 16 — Upper bound on s

There is no (49, 92, 95544)-net in base 16, because

1 times m-reduction [i] would yield (49, 91, 95544)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 577893 080310 045393 923206 080471 837599 835392 922154 726746 288090 231384 419146 724552 190313 931481 004993 585888 623861 > 16⁹¹ [i]