MinT - Best Known (32, 61, s)-Nets in Base 16

Best Known (32, 61, s)-Nets in Base 16

(32, 61, 516)-Net over F₁₆ — Constructive and digital

Digital (32, 61, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (32, 62, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 31, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(32, 61, 578)-Net over F₁₆ — Digital

Digital (32, 61, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (32, 62, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 31, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(32, 61, 58321)-Net in Base 16 — Upper bound on s

There is no (32, 61, 58322)-net in base 16, because

1 times m-reduction [i] would yield (32, 60, 58322)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 767249 432763 301019 246889 376479 185301 940436 047416 322466 495895 192034 324296 > 16⁶⁰ [i]