MinT - Best Known (74−36, 74, s)-Nets in Base 16

Best Known (74−36, 74, s)-Nets in Base 16

(74−36, 74, 516)-Net over F₁₆ — Constructive and digital

Digital (38, 74, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 37, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(74−36, 74, 578)-Net over F₁₆ — Digital

Digital (38, 74, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 37, 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]

(74−36, 74, 44896)-Net in Base 16 — Upper bound on s

There is no (38, 74, 44897)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 127321 603894 296909 532739 127028 160250 659430 207866 496294 097237 962047 861808 800393 320126 615216 > 16⁷⁴ [i]