MinT - Best Known (132−46, 132, s)-Nets in Base 5

Best Known (132−46, 132, s)-Nets in Base 5

(132−46, 132, 296)-Net over F₅ — Constructive and digital

Digital (86, 132, 296)-net over F₅, using

2 times m-reduction [i] based on digital (86, 134, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 67, 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]

(132−46, 132, 493)-Net over F₅ — Digital

Digital (86, 132, 493)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−46, 132, 24186)-Net in Base 5 — Upper bound on s

There is no (86, 132, 24187)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 731996 461750 684574 472534 230841 596407 359464 094723 165189 266564 725449 133781 481182 154248 339925 > 5¹³² [i]