MinT - Best Known (143−59, 143, s)-Nets in Base 5

Best Known (143−59, 143, s)-Nets in Base 5

(143−59, 143, 252)-Net over F₅ — Constructive and digital

Digital (84, 143, 252)-net over F₅, using

5 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(143−59, 143, 275)-Net over F₅ — Digital

Digital (84, 143, 275)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−59, 143, 7698)-Net in Base 5 — Upper bound on s

There is no (84, 143, 7699)-net in base 5, because

1 times m-reduction [i] would yield (84, 142, 7699)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1796 703139 045388 220941 280189 884897 814239 782704 740838 103213 358469 785285 043080 483418 254746 859499 082205 > 5¹⁴² [i]