MinT - Best Known (112, 112+71, s)-Nets in Base 3

Best Known (112, 112+71, s)-Nets in Base 3

(112, 112+71, 148)-Net over F₃ — Constructive and digital

Digital (112, 183, 148)-net over F₃, using

7 times m-reduction [i] based on digital (112, 190, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 95, 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]

(112, 112+71, 189)-Net over F₃ — Digital

Digital (112, 183, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+71, 2070)-Net in Base 3 — Upper bound on s

There is no (112, 183, 2071)-net in base 3, because

1 times m-reduction [i] would yield (112, 182, 2071)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 687 956990 144835 045633 560401 126410 543540 657415 216293 380522 756555 562853 237104 119504 736027 > 3¹⁸² [i]