MinT - Best Known (141−51, 141, s)-Nets in Base 5

Best Known (141−51, 141, s)-Nets in Base 5

(141−51, 141, 296)-Net over F₅ — Constructive and digital

Digital (90, 141, 296)-net over F₅, using

1 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 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]

(141−51, 141, 446)-Net over F₅ — Digital

Digital (90, 141, 446)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−51, 141, 20864)-Net in Base 5 — Upper bound on s

There is no (90, 141, 20865)-net in base 5, because

1 times m-reduction [i] would yield (90, 140, 20865)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 746928 582182 481989 436506 593281 952538 510873 361928 031550 451285 881970 427528 643998 354544 857612 429861 > 5¹⁴⁰ [i]