MinT - Best Known (124−81, 124, s)-Nets in Base 16

Best Known (124−81, 124, s)-Nets in Base 16

(124−81, 124, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 124, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 124, 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]

(124−81, 124, 226)-Net over F₁₆ — Digital

Digital (43, 124, 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]

(124−81, 124, 5278)-Net in Base 16 — Upper bound on s

There is no (43, 124, 5279)-net in base 16, because

1 times m-reduction [i] would yield (43, 123, 5279)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12787 576758 187413 064773 258459 619513 739251 059336 005839 509233 400876 713771 209213 809494 137389 299041 586720 293535 535210 204798 604945 353544 753646 397807 844276 > 16¹²³ [i]