MinT - Best Known (53, 102, s)-Nets in Base 16

Best Known (53, 102, s)-Nets in Base 16

(53, 102, 518)-Net over F₁₆ — Constructive and digital

Digital (53, 102, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 51, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(53, 102, 642)-Net over F₁₆ — Digital

Digital (53, 102, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 51, 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]

(53, 102, 76301)-Net in Base 16 — Upper bound on s

There is no (53, 102, 76302)-net in base 16, because

1 times m-reduction [i] would yield (53, 101, 76302)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 317680 449800 620245 013090 298828 543889 420602 786480 583058 356858 491851 967629 168473 851510 852532 535721 457578 821308 622326 300896 > 16¹⁰¹ [i]