MinT - Best Known (174−45, 174, s)-Nets in Base 3

Best Known (174−45, 174, s)-Nets in Base 3

(174−45, 174, 288)-Net over F₃ — Constructive and digital

Digital (129, 174, 288)-net over F₃, using

3 times m-reduction [i] based on digital (129, 177, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 59, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(174−45, 174, 665)-Net over F₃ — Digital

Digital (129, 174, 665)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−45, 174, 25548)-Net in Base 3 — Upper bound on s

There is no (129, 174, 25549)-net in base 3, because

1 times m-reduction [i] would yield (129, 173, 25549)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34846 032101 626724 957603 540876 458769 639581 303302 895442 511099 262674 236786 916212 852817 > 3¹⁷³ [i]