MinT - Best Known (126−39, 126, s)-Nets in Base 5

Best Known (126−39, 126, s)-Nets in Base 5

(126−39, 126, 296)-Net over F₅ — Constructive and digital

Digital (87, 126, 296)-net over F₅, using

10 times m-reduction [i] based on digital (87, 136, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 68, 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]

(126−39, 126, 799)-Net over F₅ — Digital

Digital (87, 126, 799)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−39, 126, 78626)-Net in Base 5 — Upper bound on s

There is no (87, 126, 78627)-net in base 5, because

1 times m-reduction [i] would yield (87, 125, 78627)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2351 529387 308243 373068 494621 898294 580030 224026 523079 530449 942363 853561 427348 242899 397125 > 5¹²⁵ [i]