MinT - Best Known (132, 132+55, s)-Nets in Base 3

Best Known (132, 132+55, s)-Nets in Base 3

(132, 132+55, 246)-Net over F₃ — Constructive and digital

Digital (132, 187, 246)-net over F₃, using

3¹ times duplication [i] based on digital (131, 186, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 62, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(132, 132+55, 446)-Net over F₃ — Digital

Digital (132, 187, 446)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+55, 10546)-Net in Base 3 — Upper bound on s

There is no (132, 187, 10547)-net in base 3, because

1 times m-reduction [i] would yield (132, 186, 10547)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55552 437931 588680 329213 459928 750185 493658 201314 673158 828276 005249 235138 959092 427459 533755 > 3¹⁸⁶ [i]