MinT - Best Known (44, 119, s)-Nets in Base 16

Best Known (44, 119, s)-Nets in Base 16

(44, 119, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 119, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 119, 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]

(44, 119, 226)-Net over F₁₆ — Digital

Digital (44, 119, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 119, 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]

(44, 119, 6740)-Net in Base 16 — Upper bound on s

There is no (44, 119, 6741)-net in base 16, because

1 times m-reduction [i] would yield (44, 118, 6741)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12249 455472 756616 182529 425205 229375 097458 630784 655651 247225 260504 435199 285627 641177 293341 960394 044038 185625 449576 953103 318183 676780 741102 065856 > 16¹¹⁸ [i]