MinT - Best Known (92−30, 92, s)-Nets in Base 9

Best Known (92−30, 92, s)-Nets in Base 9

(92−30, 92, 740)-Net over F₉ — Constructive and digital

Digital (62, 92, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 46, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(92−30, 92, 1568)-Net over F₉ — Digital

Digital (62, 92, 1568)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−30, 92, 571949)-Net in Base 9 — Upper bound on s

There is no (62, 92, 571950)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6170 526790 640591 985017 250659 011586 620060 139541 058068 660808 728803 499936 991635 362972 138961 > 9⁹² [i]