MinT - Best Known (18, ∞, s)-Nets in Base 3

Best Known (18, ∞, s)-Nets in Base 3

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

Digital (18, m, 28)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (18, 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]

(18, ∞, 45)-Net in Base 3 — Upper bound on s

There is no (18, m, 46)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (18, 179, 46)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁷⁹, 46, S₃, 4, 161), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 27 273371 522594 140467 153112 393800 633219 287891 860116 798827 111671 686466 135591 950100 031709 > 3¹⁷⁹ [i]