MinT - Best Known (63, 63+55, s)-Nets in Base 16

Best Known (63, 63+55, s)-Nets in Base 16

(63, 63+55, 522)-Net over F₁₆ — Constructive and digital

Digital (63, 118, 522)-net over F₁₆, using

trace code for nets [i] based on digital (4, 59, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(63, 63+55, 642)-Net over F₁₆ — Digital

Digital (63, 118, 642)-net over F₁₆, using

4 times m-reduction [i] based on digital (63, 122, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 61, 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]

(63, 63+55, 120258)-Net in Base 16 — Upper bound on s

There is no (63, 118, 120259)-net in base 16, because

1 times m-reduction [i] would yield (63, 117, 120259)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 762 252815 623245 221351 470677 817123 692148 249434 816266 193880 304716 567571 182395 013174 646495 424838 276107 963169 750679 184361 860083 464951 183666 136896 > 16¹¹⁷ [i]