MinT - Best Known (86−39, 86, s)-Nets in Base 5

Best Known (86−39, 86, s)-Nets in Base 5

(86−39, 86, 132)-Net over F₅ — Constructive and digital

Digital (47, 86, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 43, 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]

(86−39, 86, 2641)-Net in Base 5 — Upper bound on s

There is no (47, 86, 2642)-net in base 5, because

1 times m-reduction [i] would yield (47, 85, 2642)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 259132 543070 737766 576048 352057 003745 884797 514432 036180 347625 > 5⁸⁵ [i]