MinT - Best Known (52, 99, s)-Nets in Base 16

Best Known (52, 99, s)-Nets in Base 16

(52, 99, 518)-Net over F₁₆ — Constructive and digital

Digital (52, 99, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (52, 100, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 50, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(52, 99, 642)-Net over F₁₆ — Digital

Digital (52, 99, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (52, 100, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 50, 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]

(52, 99, 84898)-Net in Base 16 — Upper bound on s

There is no (52, 99, 84899)-net in base 16, because

1 times m-reduction [i] would yield (52, 98, 84899)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10088 769359 239449 272299 046704 562083 705713 714345 122902 947888 963080 876366 498265 322458 345160 960245 686144 374181 332834 442656 > 16⁹⁸ [i]