MinT - Best Known (78−35, 78, s)-Nets in Base 5

Best Known (78−35, 78, s)-Nets in Base 5

(78−35, 78, 132)-Net over F₅ — Constructive and digital

Digital (43, 78, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 39, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(78−35, 78, 2616)-Net in Base 5 — Upper bound on s

There is no (43, 78, 2617)-net in base 5, because

1 times m-reduction [i] would yield (43, 77, 2617)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 662270 276737 309475 389212 251421 675627 807178 831434 469285 > 5⁷⁷ [i]