MinT - Best Known (146−33, 146, s)-Nets in Base 3

Best Known (146−33, 146, s)-Nets in Base 3

(146−33, 146, 464)-Net over F₃ — Constructive and digital

Digital (113, 146, 464)-net over F₃, using

2 times m-reduction [i] based on digital (113, 148, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 37, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(146−33, 146, 977)-Net over F₃ — Digital

Digital (113, 146, 977)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−33, 146, 71668)-Net in Base 3 — Upper bound on s

There is no (113, 146, 71669)-net in base 3, because

1 times m-reduction [i] would yield (113, 145, 71669)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1522 875384 466485 326012 462584 747242 340268 247948 330991 211704 031134 698945 > 3¹⁴⁵ [i]