MinT - Best Known (44, 44+55, s)-Nets in Base 16

Best Known (44, 44+55, s)-Nets in Base 16

(44, 44+55, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 99, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 99, 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, 44+55, 226)-Net over F₁₆ — Digital

Digital (44, 99, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 99, 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, 44+55, 17078)-Net in Base 16 — Upper bound on s

There is no (44, 99, 17079)-net in base 16, because

1 times m-reduction [i] would yield (44, 98, 17079)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10095 356976 806883 782259 493820 531652 795192 800737 484319 041295 657484 480090 397580 997452 418137 531421 889197 250913 896105 940496 > 16⁹⁸ [i]