MinT - Best Known (169−64, 169, s)-Nets in Base 3

Best Known (169−64, 169, s)-Nets in Base 3

(169−64, 169, 148)-Net over F₃ — Constructive and digital

Digital (105, 169, 148)-net over F₃, using

7 times m-reduction [i] based on digital (105, 176, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 88, 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]

(169−64, 169, 189)-Net over F₃ — Digital

Digital (105, 169, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−64, 169, 2085)-Net in Base 3 — Upper bound on s

There is no (105, 169, 2086)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 434 373142 903108 224953 921931 973406 609917 451492 578702 755090 751649 499692 765391 814977 > 3¹⁶⁹ [i]