MinT - Best Known (17, ∞, s)-Nets in Base 3

Best Known (17, ∞, s)-Nets in Base 3

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

Digital (17, m, 28)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (17, 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]

(17, ∞, 43)-Net in Base 3 — Upper bound on s

There is no (17, m, 44)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (17, 171, 44)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁷¹, 44, S₃, 4, 154), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 685027 211508 324515 777792 095033 732379 709657 564813 491328 565171 830353 981268 593042 103819 / 155 > 3¹⁷¹ [i]