MinT - Best Known (114−53, 114, s)-Nets in Base 16

Best Known (114−53, 114, s)-Nets in Base 16

(114−53, 114, 522)-Net over F₁₆ — Constructive and digital

Digital (61, 114, 522)-net over F₁₆, using

trace code for nets [i] based on digital (4, 57, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(114−53, 114, 642)-Net over F₁₆ — Digital

Digital (61, 114, 642)-net over F₁₆, using

4 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]

(114−53, 114, 120348)-Net in Base 16 — Upper bound on s

There is no (61, 114, 120349)-net in base 16, because

1 times m-reduction [i] would yield (61, 113, 120349)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11630 373388 501736 295494 826847 541873 914417 686952 611933 619739 514004 851548 289853 886561 263265 333797 495666 601435 489263 285349 723812 563317 732986 > 16¹¹³ [i]