MinT - Best Known (142, 142+79, s)-Nets in Base 3

Best Known (142, 142+79, s)-Nets in Base 3

(142, 142+79, 156)-Net over F₃ — Constructive and digital

Digital (142, 221, 156)-net over F₃, using

19 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, 142+79, 281)-Net over F₃ — Digital

Digital (142, 221, 281)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+79, 3744)-Net in Base 3 — Upper bound on s

There is no (142, 221, 3745)-net in base 3, because

1 times m-reduction [i] would yield (142, 220, 3745)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 928 351066 674538 924325 463436 325377 141160 207390 428547 632109 093007 240235 780114 290790 782764 546490 661143 208587 > 3²²⁰ [i]