MinT - Best Known (16, ∞, s)-Nets in Base 3

Best Known (16, ∞, s)-Nets in Base 3

(16, ∞, 28)-Net over F₃ — Constructive and digital

Digital (16, m, 28)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (16, 27)-sequence over F₃, using
- t-expansion [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]

(16, ∞, 41)-Net in Base 3 — Upper bound on s

There is no (16, m, 42)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (16, 163, 42)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁶³, 42, S₃, 4, 147), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 26 544651 814199 643338 440247 651133 135698 218965 877468 993535 187581 097625 462811 569215 / 37 > 3¹⁶³ [i]