MinT - Best Known (121, 121+79, s)-Nets in Base 3

Best Known (121, 121+79, s)-Nets in Base 3

(121, 121+79, 148)-Net over F₃ — Constructive and digital

Digital (121, 200, 148)-net over F₃, using

8 times m-reduction [i] based on digital (121, 208, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 104, 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]

(121, 121+79, 194)-Net over F₃ — Digital

Digital (121, 200, 194)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+79, 2055)-Net in Base 3 — Upper bound on s

There is no (121, 200, 2056)-net in base 3, because

1 times m-reduction [i] would yield (121, 199, 2056)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 89197 583724 264073 127455 244839 315991 567895 375571 079628 910964 978645 708201 172738 704445 585793 959777 > 3¹⁹⁹ [i]