MinT - Best Known (85−37, 85, s)-Nets in Base 5

Best Known (85−37, 85, s)-Nets in Base 5

(85−37, 85, 132)-Net over F₅ — Constructive and digital

Digital (48, 85, 132)-net over F₅, using

3 times m-reduction [i] based on digital (48, 88, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 44, 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]

(85−37, 85, 149)-Net over F₅ — Digital

Digital (48, 85, 149)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−37, 85, 3437)-Net in Base 5 — Upper bound on s

There is no (48, 85, 3438)-net in base 5, because

1 times m-reduction [i] would yield (48, 84, 3438)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51725 886803 751229 913409 108144 336713 197330 015457 479716 186625 > 5⁸⁴ [i]