MinT - Best Known (139−47, 139, s)-Nets in Base 5

Best Known (139−47, 139, s)-Nets in Base 5

(139−47, 139, 296)-Net over F₅ — Constructive and digital

Digital (92, 139, 296)-net over F₅, using

7 times m-reduction [i] based on digital (92, 146, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 73, 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]

(139−47, 139, 585)-Net over F₅ — Digital

Digital (92, 139, 585)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−47, 139, 36814)-Net in Base 5 — Upper bound on s

There is no (92, 139, 36815)-net in base 5, because

1 times m-reduction [i] would yield (92, 138, 36815)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 870772 472417 259047 101135 499431 454350 874654 586472 942049 360026 528576 526366 167213 646775 138330 268645 > 5¹³⁸ [i]