MinT - Best Known (115−54, 115, s)-Nets in Base 5

Best Known (115−54, 115, s)-Nets in Base 5

(115−54, 115, 104)-Net over F₅ — Constructive and digital

Digital (61, 115, 104)-net over F₅, using

1 times m-reduction [i] based on digital (61, 116, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 58, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(115−54, 115, 144)-Net over F₅ — Digital

Digital (61, 115, 144)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−54, 115, 2571)-Net in Base 5 — Upper bound on s

There is no (61, 115, 2572)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 242 888721 601949 312439 162520 274039 707886 436441 013549 627053 244555 822738 719671 583025 > 5¹¹⁵ [i]