MinT - Best Known (18, 18+14, s)-Nets in Base 16

Best Known (18, 18+14, s)-Nets in Base 16

(18, 18+14, 518)-Net over F₁₆ — Constructive and digital

Digital (18, 32, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 16, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(18, 18+14, 642)-Net over F₁₆ — Digital

Digital (18, 32, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 16, 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]

(18, 18+14, 72003)-Net in Base 16 — Upper bound on s

There is no (18, 32, 72004)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 340 291420 095942 040405 598637 963982 973296 > 16³² [i]