MinT - Best Known (140−47, 140, s)-Nets in Base 5

Best Known (140−47, 140, s)-Nets in Base 5

(140−47, 140, 296)-Net over F₅ — Constructive and digital

Digital (93, 140, 296)-net over F₅, using

8 times m-reduction [i] based on digital (93, 148, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 74, 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]

(140−47, 140, 607)-Net over F₅ — Digital

Digital (93, 140, 607)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−47, 140, 39484)-Net in Base 5 — Upper bound on s

There is no (93, 140, 39485)-net in base 5, because

1 times m-reduction [i] would yield (93, 139, 39485)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 356892 729163 940884 344615 726692 501009 449310 917545 408274 610184 449715 736466 318558 887562 870473 545885 > 5¹³⁹ [i]