MinT - Best Known (15, 15+∞, s)-Nets in Base 3

Best Known (15, 15+∞, s)-Nets in Base 3

(15, 15+∞, 28)-Net over F₃ — Constructive and digital

Digital (15, m, 28)-net over F₃ for arbitrarily large m, 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]

(15, 15+∞, 39)-Net in Base 3 — Upper bound on s

There is no (15, m, 40)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (15, 155, 40)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁵⁵, 40, S₃, 4, 140), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 5484 339313 675687 119662 839698 281499 356776 090767 076863 640862 478439 787814 294927 / 47 > 3¹⁵⁵ [i]