MinT - Best Known (64, 64+58, s)-Nets in Base 16

Best Known (64, 64+58, s)-Nets in Base 16

(64, 64+58, 520)-Net over F₁₆ — Constructive and digital

Digital (64, 122, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 61, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(64, 64+58, 642)-Net over F₁₆ — Digital

Digital (64, 122, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (64, 124, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 62, 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]

(64, 64+58, 90482)-Net in Base 16 — Upper bound on s

There is no (64, 122, 90483)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 799 406999 079721 960469 857109 476085 138013 835493 667757 306320 620605 411258 706776 648642 905272 321920 801009 220358 066376 827487 416543 577644 414844 099217 797456 > 16¹²² [i]