MinT - Best Known (43, 43+75, s)-Nets in Base 16

Best Known (43, 43+75, s)-Nets in Base 16

(43, 43+75, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 118, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 118, 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]

(43, 43+75, 226)-Net over F₁₆ — Digital

Digital (43, 118, 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]

(43, 43+75, 6252)-Net in Base 16 — Upper bound on s

There is no (43, 118, 6253)-net in base 16, because

1 times m-reduction [i] would yield (43, 117, 6253)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 766 263518 012640 639675 188801 184401 603725 665923 532941 728215 088967 609193 929650 006877 875839 800787 996813 805965 607124 980107 022142 575417 105892 907016 > 16¹¹⁷ [i]