MinT - Best Known (75, 75+66, s)-Nets in Base 5

Best Known (75, 75+66, s)-Nets in Base 5

(75, 75+66, 132)-Net over F₅ — Constructive and digital

Digital (75, 141, 132)-net over F₅, using

1 times m-reduction [i] based on digital (75, 142, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 71, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(75, 75+66, 173)-Net over F₅ — Digital

Digital (75, 141, 173)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+66, 3165)-Net in Base 5 — Upper bound on s

There is no (75, 141, 3166)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 359 099359 280356 906651 083877 981857 925586 484384 801445 611570 307980 160412 277690 960449 054390 621999 935865 > 5¹⁴¹ [i]