MinT - Best Known (40, 121, s)-Nets in Base 16

Best Known (40, 121, s)-Nets in Base 16

(40, 121, 225)-Net over F₁₆ — Constructive and digital

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]

(40, 121, 4283)-Net in Base 16 — Upper bound on s

There is no (40, 121, 4284)-net in base 16, because

1 times m-reduction [i] would yield (40, 120, 4284)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 129856 879637 126398 133788 371279 710331 250897 553503 798835 960417 097635 121007 487081 128903 768142 883693 740929 276952 613638 385664 830016 919657 668188 005401 > 16¹²⁰ [i]