MinT - Best Known (85−23, 85, s)-Nets in Base 5

Best Known (85−23, 85, s)-Nets in Base 5

(85−23, 85, 296)-Net over F₅ — Constructive and digital

Digital (62, 85, 296)-net over F₅, using

1 times m-reduction [i] based on digital (62, 86, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 43, 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]

(85−23, 85, 1147)-Net over F₅ — Digital

Digital (62, 85, 1147)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−23, 85, 267011)-Net in Base 5 — Upper bound on s

There is no (62, 85, 267012)-net in base 5, because

1 times m-reduction [i] would yield (62, 84, 267012)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51698 913917 092975 632712 154055 405312 074552 863112 756771 169809 > 5⁸⁴ [i]