MinT - Best Known (91−39, 91, s)-Nets in Base 5

Best Known (91−39, 91, s)-Nets in Base 5

(91−39, 91, 132)-Net over F₅ — Constructive and digital

Digital (52, 91, 132)-net over F₅, using

5 times m-reduction [i] based on digital (52, 96, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 48, 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]

(91−39, 91, 165)-Net over F₅ — Digital

Digital (52, 91, 165)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−39, 91, 4041)-Net in Base 5 — Upper bound on s

There is no (52, 91, 4042)-net in base 5, because

1 times m-reduction [i] would yield (52, 90, 4042)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 807 910586 236917 240612 932528 911297 373764 113249 898284 755396 532425 > 5⁹⁰ [i]