MinT - Best Known (122, 122+87, s)-Nets in Base 3

Best Known (122, 122+87, s)-Nets in Base 3

(122, 122+87, 148)-Net over F₃ — Constructive and digital

Digital (122, 209, 148)-net over F₃, using

1 times m-reduction [i] based on digital (122, 210, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 105, 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]

(122, 122+87, 174)-Net over F₃ — Digital

Digital (122, 209, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+87, 1673)-Net in Base 3 — Upper bound on s

There is no (122, 209, 1674)-net in base 3, because

1 times m-reduction [i] would yield (122, 208, 1674)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1770 562474 951329 522957 000023 556218 428023 843459 924819 660144 596196 013426 038993 408533 441715 343524 161825 > 3²⁰⁸ [i]