MinT - Best Known (188−55, 188, s)-Nets in Base 3

Best Known (188−55, 188, s)-Nets in Base 3

(188−55, 188, 246)-Net over F₃ — Constructive and digital

Digital (133, 188, 246)-net over F₃, using

1 times m-reduction [i] based on digital (133, 189, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 63, 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]

(188−55, 188, 456)-Net over F₃ — Digital

Digital (133, 188, 456)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−55, 188, 10985)-Net in Base 3 — Upper bound on s

There is no (133, 188, 10986)-net in base 3, because

1 times m-reduction [i] would yield (133, 187, 10986)-net in base 3, but
- 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]