MinT - Best Known (122−80, 122, s)-Nets in Base 16

Best Known (122−80, 122, s)-Nets in Base 16

(122−80, 122, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 122, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 122, 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]

(122−80, 122, 4923)-Net in Base 16 — Upper bound on s

There is no (42, 122, 4924)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 799 224088 716462 720622 457812 029330 847600 872671 857840 697071 322858 774897 750883 006564 449151 791516 309445 686309 919225 154616 657537 622258 086829 148721 316901 > 16¹²² [i]