MinT - Best Known (30, 56, s)-Nets in Base 16

Best Known (30, 56, s)-Nets in Base 16

(30, 56, 518)-Net over F₁₆ — Constructive and digital

Digital (30, 56, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 28, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(30, 56, 642)-Net over F₁₆ — Digital

Digital (30, 56, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 28, 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]

(30, 56, 58108)-Net in Base 16 — Upper bound on s

There is no (30, 56, 58109)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 26 961085 493676 750505 003400 392311 067018 206970 089703 347885 528735 372256 > 16⁵⁶ [i]