MinT - Best Known (76−36, 76, s)-Nets in Base 16

Best Known (76−36, 76, s)-Nets in Base 16

(76−36, 76, 518)-Net over F₁₆ — Constructive and digital

Digital (40, 76, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 38, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(76−36, 76, 642)-Net over F₁₆ — Digital

Digital (40, 76, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 38, 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]

(76−36, 76, 61098)-Net in Base 16 — Upper bound on s

There is no (40, 76, 61099)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 32 595406 283907 432573 117970 456477 650354 308408 200096 352318 712295 921186 023773 778022 291037 991106 > 16⁷⁶ [i]