MinT - Best Known (105, 105+69, s)-Nets in Base 3

Best Known (105, 105+69, s)-Nets in Base 3

(105, 105+69, 148)-Net over F₃ — Constructive and digital

Digital (105, 174, 148)-net over F₃, using

2 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]

(105, 105+69, 170)-Net over F₃ — Digital

Digital (105, 174, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+69, 1778)-Net in Base 3 — Upper bound on s

There is no (105, 174, 1779)-net in base 3, because

1 times m-reduction [i] would yield (105, 173, 1779)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35012 386137 119210 538836 769866 040226 530559 170407 310351 681740 045735 752764 710161 908165 > 3¹⁷³ [i]