MinT - Best Known (89−73, 89, s)-Nets in Base 3

Best Known (89−73, 89, s)-Nets in Base 3

(89−73, 89, 28)-Net over F₃ — Constructive and digital

Digital (16, 89, 28)-net over F₃, using

t-expansion [i] based on digital (15, 89, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(89−73, 89, 44)-Net in Base 3 — Upper bound on s

There is no (16, 89, 45)-net in base 3, because

3 times m-reduction [i] would yield (16, 86, 45)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3⁸⁶, 45, S₃, 2, 70), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 8 727963 568087 712425 891397 479476 727340 041449 / 71 > 3⁸⁶ [i]