MinT - Best Known (27, 42, s)-Nets in Base 5

Best Known (27, 42, s)-Nets in Base 5

(27, 42, 132)-Net over F₅ — Constructive and digital

Digital (27, 42, 132)-net over F₅, using

4 times m-reduction [i] based on digital (27, 46, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 23, 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]

(27, 42, 196)-Net over F₅ — Digital

Digital (27, 42, 196)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 42, 10486)-Net in Base 5 — Upper bound on s

There is no (27, 42, 10487)-net in base 5, because

1 times m-reduction [i] would yield (27, 41, 10487)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45490 918048 342163 704323 876165 > 5⁴¹ [i]