MinT - Best Known (43, 104, s)-Nets in Base 16

Best Known (43, 104, s)-Nets in Base 16

(43, 104, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 104, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 104, 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, 104, 226)-Net over F₁₆ — Digital

Digital (43, 104, 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, 104, 10919)-Net in Base 16 — Upper bound on s

There is no (43, 104, 10920)-net in base 16, because

1 times m-reduction [i] would yield (43, 103, 10920)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10602 809750 494348 182314 330002 584131 526707 189113 088193 853086 837197 619710 044415 768707 159753 518618 357648 521067 199550 734095 820876 > 16¹⁰³ [i]