MinT - Best Known (61, 61+45, s)-Nets in Base 5

Best Known (61, 61+45, s)-Nets in Base 5

(61, 61+45, 132)-Net over F₅ — Constructive and digital

Digital (61, 106, 132)-net over F₅, using

8 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, 61+45, 194)-Net over F₅ — Digital

Digital (61, 106, 194)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+45, 4890)-Net in Base 5 — Upper bound on s

There is no (61, 106, 4891)-net in base 5, because

1 times m-reduction [i] would yield (61, 105, 4891)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 24 687091 146030 103245 650813 019794 294757 474843 482033 380231 423431 074625 011625 > 5¹⁰⁵ [i]