MinT - Best Known (142, 235, s)-Nets in Base 3

Best Known (142, 235, s)-Nets in Base 3

(142, 235, 156)-Net over F₃ — Constructive and digital

Digital (142, 235, 156)-net over F₃, using

5 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, 235, 222)-Net over F₃ — Digital

Digital (142, 235, 222)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 235, 2360)-Net in Base 3 — Upper bound on s

There is no (142, 235, 2361)-net in base 3, because

1 times m-reduction [i] would yield (142, 234, 2361)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4442 317313 759646 244670 010788 477789 617571 598039 578215 578750 659350 096939 573497 793322 431016 339413 123515 071168 930217 > 3²³⁴ [i]