MinT - Best Known (133−39, 133, s)-Nets in Base 3

Best Known (133−39, 133, s)-Nets in Base 3

(133−39, 133, 204)-Net over F₃ — Constructive and digital

Digital (94, 133, 204)-net over F₃, using

3¹ times duplication [i] based on digital (93, 132, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 44, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(133−39, 133, 340)-Net over F₃ — Digital

Digital (94, 133, 340)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−39, 133, 8164)-Net in Base 3 — Upper bound on s

There is no (94, 133, 8165)-net in base 3, because

1 times m-reduction [i] would yield (94, 132, 8165)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 955 653194 899060 862210 460321 076234 052635 190495 009410 515366 355371 > 3¹³² [i]