MinT - Best Known (96−46, 96, s)-Nets in Base 16

Best Known (96−46, 96, s)-Nets in Base 16

(96−46, 96, 518)-Net over F₁₆ — Constructive and digital

Digital (50, 96, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 48, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(96−46, 96, 642)-Net over F₁₆ — Digital

Digital (50, 96, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 48, 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]

(96−46, 96, 66707)-Net in Base 16 — Upper bound on s

There is no (50, 96, 66708)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 406979 827233 772829 937611 613033 367157 503296 648990 006279 599446 557515 579149 818092 088198 031222 058801 795169 435718 387936 > 16⁹⁶ [i]