MinT - Best Known (107−64, 107, s)-Nets in Base 16

Best Known (107−64, 107, s)-Nets in Base 16

(107−64, 107, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 107, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 107, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(107−64, 107, 226)-Net over F₁₆ — Digital

Digital (43, 107, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(107−64, 107, 9041)-Net in Base 16 — Upper bound on s

There is no (43, 107, 9042)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 695 464927 351773 408058 159721 197067 454114 948184 991544 556026 282865 306352 366087 328555 878665 000848 264121 328720 402494 392823 673204 040586 > 16¹⁰⁷ [i]