MinT - Best Known (187−54, 187, s)-Nets in Base 3

Best Known (187−54, 187, s)-Nets in Base 3

(187−54, 187, 252)-Net over F₃ — Constructive and digital

Digital (133, 187, 252)-net over F₃, using

3¹ times duplication [i] based on digital (132, 186, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 62, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(187−54, 187, 474)-Net over F₃ — Digital

Digital (133, 187, 474)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−54, 187, 10985)-Net in Base 3 — Upper bound on s

There is no (133, 187, 10986)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166616 735986 938886 586771 520961 503687 702681 644030 478144 060067 612487 671412 141189 440754 732609 > 3¹⁸⁷ [i]