MinT - Best Known (92−41, 92, s)-Nets in Base 3

Best Known (92−41, 92, s)-Nets in Base 3

(92−41, 92, 64)-Net over F₃ — Constructive and digital

Digital (51, 92, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 46, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(92−41, 92, 73)-Net over F₃ — Digital

Digital (51, 92, 73)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−41, 92, 596)-Net in Base 3 — Upper bound on s

There is no (51, 92, 597)-net in base 3, because

1 times m-reduction [i] would yield (51, 91, 597)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 888079 209080 609147 131069 889729 289400 736401 > 3⁹¹ [i]