MinT - Best Known (145−39, 145, s)-Nets in Base 5

Best Known (145−39, 145, s)-Nets in Base 5

(145−39, 145, 408)-Net over F₅ — Constructive and digital

Digital (106, 145, 408)-net over F₅, using

t-expansion [i] based on digital (105, 145, 408)-net over F₅, using
- 5 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
  - trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
    - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
        a function field by GarcÃa and Quoos [i]

(145−39, 145, 1764)-Net over F₅ — Digital

Digital (106, 145, 1764)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−39, 145, 393185)-Net in Base 5 — Upper bound on s

There is no (106, 145, 393186)-net in base 5, because

1 times m-reduction [i] would yield (106, 144, 393186)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44843 204315 032387 484388 410359 946990 582540 505659 393268 200576 090500 999690 909307 482580 851031 341016 573225 > 5¹⁴⁴ [i]