MinT - Best Known (186, 186+61, s)-Nets in Base 3

Best Known (186, 186+61, s)-Nets in Base 3

(186, 186+61, 328)-Net over F₃ — Constructive and digital

Digital (186, 247, 328)-net over F₃, using

1 times m-reduction [i] based on digital (186, 248, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 62, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(186, 186+61, 1062)-Net over F₃ — Digital

Digital (186, 247, 1062)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+61, 49191)-Net in Base 3 — Upper bound on s

There is no (186, 247, 49192)-net in base 3, because

1 times m-reduction [i] would yield (186, 246, 49192)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 415855 810326 672106 296207 906905 049173 645908 591359 864627 167737 149463 676029 094002 673750 161024 334808 799602 891873 374833 > 3²⁴⁶ [i]