MinT - Best Known (54, 54+50, s)-Nets in Base 16

Best Known (54, 54+50, s)-Nets in Base 16

(54, 54+50, 518)-Net over F₁₆ — Constructive and digital

Digital (54, 104, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 52, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(54, 54+50, 642)-Net over F₁₆ — Digital

Digital (54, 104, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 52, 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]

(54, 54+50, 69276)-Net in Base 16 — Upper bound on s

There is no (54, 104, 69277)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169240 455819 968562 754643 841984 108102 006054 688334 058640 810831 160707 322009 911622 629132 678311 929827 683954 706310 318817 521989 543876 > 16¹⁰⁴ [i]