MinT - Best Known (141−67, 141, s)-Nets in Base 5

Best Known (141−67, 141, s)-Nets in Base 5

(141−67, 141, 104)-Net over F₅ — Constructive and digital

Digital (74, 141, 104)-net over F₅, using

1 times m-reduction [i] based on digital (74, 142, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 71, 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]

(141−67, 141, 165)-Net over F₅ — Digital

Digital (74, 141, 165)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−67, 141, 3014)-Net in Base 5 — Upper bound on s

There is no (74, 141, 3015)-net in base 5, because

1 times m-reduction [i] would yield (74, 140, 3015)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 72 487146 983498 110513 456406 094780 334568 728939 294617 934143 308662 380396 638795 291934 248494 946545 028765 > 5¹⁴⁰ [i]