MinT - Best Known (169−68, 169, s)-Nets in Base 3

Best Known (169−68, 169, s)-Nets in Base 3

(169−68, 169, 128)-Net over F₃ — Constructive and digital

Digital (101, 169, 128)-net over F₃, using

7 times m-reduction [i] based on digital (101, 176, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 88, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(169−68, 169, 159)-Net over F₃ — Digital

Digital (101, 169, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−68, 169, 1559)-Net in Base 3 — Upper bound on s

There is no (101, 169, 1560)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 438 662342 877838 571088 827571 513562 804066 550795 882235 370132 733793 517181 373002 583825 > 3¹⁶⁹ [i]