MinT - Best Known (42, 121, s)-Nets in Base 16

Best Known (42, 121, s)-Nets in Base 16

(42, 121, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 121, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 121, 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, 121, 5182)-Net in Base 16 — Upper bound on s

There is no (42, 121, 5183)-net in base 16, because

1 times m-reduction [i] would yield (42, 120, 5183)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 140570 182610 646924 455704 522954 394065 345611 466113 428108 188298 736430 869345 757503 517302 876220 002167 711169 777662 435888 610434 971584 317431 936948 871656 > 16¹²⁰ [i]