MinT - Best Known (119−36, 119, s)-Nets in Base 5

Best Known (119−36, 119, s)-Nets in Base 5

(119−36, 119, 296)-Net over F₅ — Constructive and digital

Digital (83, 119, 296)-net over F₅, using

9 times m-reduction [i] based on digital (83, 128, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 64, 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]

(119−36, 119, 845)-Net over F₅ — Digital

Digital (83, 119, 845)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−36, 119, 78879)-Net in Base 5 — Upper bound on s

There is no (83, 119, 78880)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150463 522051 991531 766955 025698 883202 485353 894590 014368 447644 536196 173102 393625 485825 > 5¹¹⁹ [i]