MinT - Best Known (78−30, 78, s)-Nets in Base 5

Best Known (78−30, 78, s)-Nets in Base 5

(78−30, 78, 208)-Net over F₅ — Constructive and digital

Digital (48, 78, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 39, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(78−30, 78, 220)-Net over F₅ — Digital

Digital (48, 78, 220)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−30, 78, 6913)-Net in Base 5 — Upper bound on s

There is no (48, 78, 6914)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 314790 012493 859962 030613 675660 315252 308255 332911 745065 > 5⁷⁸ [i]