MinT - Best Known (142, 142+107, s)-Nets in Base 3

Best Known (142, 142+107, s)-Nets in Base 3

(142, 142+107, 148)-Net over F₃ — Constructive and digital

Digital (142, 249, 148)-net over F₃, using

1 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(142, 142+107, 185)-Net over F₃ — Digital

Digital (142, 249, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+107, 1707)-Net in Base 3 — Upper bound on s

There is no (142, 249, 1708)-net in base 3, because

1 times m-reduction [i] would yield (142, 248, 1708)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21575 964777 759898 460044 542304 122002 378574 503677 104242 891478 139348 654013 930883 646981 147133 105454 172995 109856 135839 100217 > 3²⁴⁸ [i]