MinT - Best Known (146−70, 146, s)-Nets in Base 5

Best Known (146−70, 146, s)-Nets in Base 5

(146−70, 146, 104)-Net over F₅ — Constructive and digital

Digital (76, 146, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 73, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(146−70, 146, 164)-Net over F₅ — Digital

Digital (76, 146, 164)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−70, 146, 2837)-Net in Base 5 — Upper bound on s

There is no (76, 146, 2838)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 122427 820091 772571 520737 641554 381935 386039 648216 501682 002740 296485 183044 661152 302377 064904 235608 203897 > 5¹⁴⁶ [i]