MinT - Best Known (122−55, 122, s)-Nets in Base 5

Best Known (122−55, 122, s)-Nets in Base 5

(122−55, 122, 132)-Net over F₅ — Constructive and digital

Digital (67, 122, 132)-net over F₅, using

4 times m-reduction [i] based on digital (67, 126, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 63, 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]

(122−55, 122, 175)-Net over F₅ — Digital

Digital (67, 122, 175)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−55, 122, 3685)-Net in Base 5 — Upper bound on s

There is no (67, 122, 3686)-net in base 5, because

1 times m-reduction [i] would yield (67, 121, 3686)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 785932 733297 856968 265246 448702 728409 861464 129312 396114 577036 438542 474843 345468 889785 > 5¹²¹ [i]