MinT - Best Known (42, 95, s)-Nets in Base 16

Best Known (42, 95, s)-Nets in Base 16

(42, 95, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 95, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 95, 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]

(42, 95, 15855)-Net in Base 16 — Upper bound on s

There is no (42, 95, 15856)-net in base 16, because

1 times m-reduction [i] would yield (42, 94, 15856)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 154140 770481 014720 443518 915553 334923 189381 231370 430280 966163 304746 426108 586301 073520 299168 106724 194667 208834 994466 > 16⁹⁴ [i]