MinT - Best Known (89, 132, s)-Nets in Base 5

Best Known (89, 132, s)-Nets in Base 5

(89, 132, 296)-Net over F₅ — Constructive and digital

Digital (89, 132, 296)-net over F₅, using

8 times m-reduction [i] based on digital (89, 140, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 70, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(89, 132, 664)-Net over F₅ — Digital

Digital (89, 132, 664)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 132, 49721)-Net in Base 5 — Upper bound on s

There is no (89, 132, 49722)-net in base 5, because

1 times m-reduction [i] would yield (89, 131, 49722)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 747918 991586 809059 036043 519331 474062 865126 411003 752743 506217 271603 279366 296144 723098 853609 > 5¹³¹ [i]