MinT - Best Known (61, 108, s)-Nets in Base 5

Best Known (61, 108, s)-Nets in Base 5

(61, 108, 132)-Net over F₅ — Constructive and digital

Digital (61, 108, 132)-net over F₅, using

6 times m-reduction [i] based on digital (61, 114, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 57, 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]

(61, 108, 180)-Net over F₅ — Digital

Digital (61, 108, 180)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 108, 4191)-Net in Base 5 — Upper bound on s

There is no (61, 108, 4192)-net in base 5, because

1 times m-reduction [i] would yield (61, 107, 4192)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 617 092785 283509 046869 165319 055406 829590 990527 100852 064224 789796 393545 431425 > 5¹⁰⁷ [i]