MinT - Best Known (116−55, 116, s)-Nets in Base 16

Best Known (116−55, 116, s)-Nets in Base 16

(116−55, 116, 520)-Net over F₁₆ — Constructive and digital

Digital (61, 116, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 58, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(116−55, 116, 642)-Net over F₁₆ — Digital

Digital (61, 116, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (61, 118, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 59, 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]

(116−55, 116, 97928)-Net in Base 16 — Upper bound on s

There is no (61, 116, 97929)-net in base 16, because

1 times m-reduction [i] would yield (61, 115, 97929)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 977548 037757 546605 561284 445861 676221 664117 898699 893955 143706 536960 654844 938286 768946 608269 260703 277224 790883 995531 861612 341784 626769 498496 > 16¹¹⁵ [i]