MinT - Best Known (126, 191, s)-Nets in Base 3

Best Known (126, 191, s)-Nets in Base 3

(126, 191, 156)-Net over F₃ — Constructive and digital

Digital (126, 191, 156)-net over F₃, using

17 times m-reduction [i] based on digital (126, 208, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 104, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(126, 191, 287)-Net over F₃ — Digital

Digital (126, 191, 287)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 191, 4321)-Net in Base 3 — Upper bound on s

There is no (126, 191, 4322)-net in base 3, because

1 times m-reduction [i] would yield (126, 190, 4322)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 521878 435394 800446 408877 554287 248703 895412 444292 056848 928816 999046 525843 203292 581848 498497 > 3¹⁹⁰ [i]