MinT - Best Known (14, 14+11, s)-Nets in Base 16

Best Known (14, 14+11, s)-Nets in Base 16

(14, 14+11, 516)-Net over F₁₆ — Constructive and digital

Digital (14, 25, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (14, 26, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 13, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(14, 14+11, 578)-Net over F₁₆ — Digital

Digital (14, 25, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (14, 26, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 13, 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]

(14, 14+11, 104595)-Net in Base 16 — Upper bound on s

There is no (14, 25, 104596)-net in base 16, because

1 times m-reduction [i] would yield (14, 24, 104596)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 79231 681277 012821 937397 345076 > 16²⁴ [i]