MinT - Best Known (182, 182+51, s)-Nets in Base 3

Best Known (182, 182+51, s)-Nets in Base 3

(182, 182+51, 688)-Net over F₃ — Constructive and digital

Digital (182, 233, 688)-net over F₃, using

3¹ times duplication [i] based on digital (181, 232, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 58, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(182, 182+51, 1654)-Net over F₃ — Digital

Digital (182, 233, 1654)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 182+51, 136208)-Net in Base 3 — Upper bound on s

There is no (182, 233, 136209)-net in base 3, because

1 times m-reduction [i] would yield (182, 232, 136209)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 268360 747724 861263 631480 074636 041416 524161 703267 590678 262600 339549 092005 644017 071727 921311 986884 335617 799619 > 3²³² [i]