MinT - Best Known (38−13, 38, s)-Nets in Base 5

Best Known (38−13, 38, s)-Nets in Base 5

(38−13, 38, 132)-Net over F₅ — Constructive and digital

Digital (25, 38, 132)-net over F₅, using

4 times m-reduction [i] based on digital (25, 42, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 21, 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]

(38−13, 38, 222)-Net over F₅ — Digital

Digital (25, 38, 222)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38−13, 38, 15288)-Net in Base 5 — Upper bound on s

There is no (25, 38, 15289)-net in base 5, because

1 times m-reduction [i] would yield (25, 37, 15289)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 72 775217 863626 548366 309641 > 5³⁷ [i]