MinT - Best Known (168−144, 168, s)-Nets in Base 3

Best Known (168−144, 168, s)-Nets in Base 3

(168−144, 168, 32)-Net over F₃ — Constructive and digital

Digital (24, 168, 32)-net over F₃, using

t-expansion [i] based on digital (21, 168, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(168−144, 168, 63)-Net in Base 3 — Upper bound on s

There is no (24, 168, 64)-net in base 3, because

45 times m-reduction [i] would yield (24, 123, 64)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹²³, 64, S₃, 2, 99), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 310020 508637 620352 391208 095712 502073 964245 732475 093456 566329 / 25 > 3¹²³ [i]