MinT - Best Known (110, 170, s)-Nets in Base 3

Best Known (110, 170, s)-Nets in Base 3

(110, 170, 156)-Net over F₃ — Constructive and digital

Digital (110, 170, 156)-net over F₃, using

6 times m-reduction [i] based on digital (110, 176, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 88, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(110, 170, 233)-Net over F₃ — Digital

Digital (110, 170, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 170, 3014)-Net in Base 3 — Upper bound on s

There is no (110, 170, 3015)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1294 823760 435862 882790 539315 472617 674577 812071 735591 285739 429288 047110 045081 363221 > 3¹⁷⁰ [i]