MinT - Best Known (87−37, 87, s)-Nets in Base 5

Best Known (87−37, 87, s)-Nets in Base 5

(87−37, 87, 132)-Net over F₅ — Constructive and digital

Digital (50, 87, 132)-net over F₅, using

5 times m-reduction [i] based on digital (50, 92, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 46, 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]

(87−37, 87, 164)-Net over F₅ — Digital

Digital (50, 87, 164)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−37, 87, 4113)-Net in Base 5 — Upper bound on s

There is no (50, 87, 4114)-net in base 5, because

1 times m-reduction [i] would yield (50, 86, 4114)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 294586 828299 608716 015932 494147 730637 413257 828120 629838 105665 > 5⁸⁶ [i]