MinT - Best Known (41, 41+79, s)-Nets in Base 16

Best Known (41, 41+79, s)-Nets in Base 16

(41, 41+79, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 120, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 120, 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]

(41, 41+79, 4825)-Net in Base 16 — Upper bound on s

There is no (41, 120, 4826)-net in base 16, because

1 times m-reduction [i] would yield (41, 119, 4826)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 196532 691489 884728 126841 494401 605665 509316 019124 616406 365279 218715 933770 297338 843380 017892 283005 557291 080650 571450 169414 120852 085033 668179 470936 > 16¹¹⁹ [i]