MinT - Best Known (30, 30+28, s)-Nets in Base 16

Best Known (30, 30+28, s)-Nets in Base 16

(30, 30+28, 516)-Net over F₁₆ — Constructive and digital

Digital (30, 58, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(30, 30+28, 578)-Net over F₁₆ — Digital

Digital (30, 58, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 29, 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]

(30, 30+28, 39244)-Net in Base 16 — Upper bound on s

There is no (30, 58, 39245)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6902 420326 678168 408174 939021 218605 734555 236090 221206 174718 284909 420576 > 16⁵⁸ [i]