MinT - Best Known (177, 177+69, s)-Nets in Base 3

Best Known (177, 177+69, s)-Nets in Base 3

(177, 177+69, 288)-Net over F₃ — Constructive and digital

Digital (177, 246, 288)-net over F₃, using

3 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 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]

(177, 177+69, 663)-Net over F₃ — Digital

Digital (177, 246, 663)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+69, 18524)-Net in Base 3 — Upper bound on s

There is no (177, 246, 18525)-net in base 3, because

1 times m-reduction [i] would yield (177, 245, 18525)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 785 765197 368122 015311 795739 182924 664530 189754 651447 504245 683980 058972 947695 154118 077605 900131 932283 407136 704539 614273 > 3²⁴⁵ [i]