MinT - Best Known (142, 226, s)-Nets in Base 3

Best Known (142, 226, s)-Nets in Base 3

(142, 226, 156)-Net over F₃ — Constructive and digital

Digital (142, 226, 156)-net over F₃, using

14 times m-reduction [i] based on digital (142, 240, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 120, 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]

(142, 226, 257)-Net over F₃ — Digital

Digital (142, 226, 257)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 226, 3007)-Net in Base 3 — Upper bound on s

There is no (142, 226, 3008)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 678866 638217 269088 863796 488882 306235 121488 633445 172704 083665 174789 666547 688367 907908 388085 729939 578820 444801 > 3²²⁶ [i]