MinT - Best Known (35, ∞, s)-Nets in Base 3

Best Known (35, ∞, s)-Nets in Base 3

(35, ∞, 38)-Net over F₃ — Constructive and digital

Digital (35, m, 38)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (35, 37)-sequence over F₃, using
- t-expansion [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(35, ∞, 47)-Net over F₃ — Digital

Digital (35, m, 47)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(35, ∞, 81)-Net in Base 3 — Upper bound on s

There is no (35, m, 82)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (35, 322, 82)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3³²², 82, S₃, 4, 287), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 21478 998321 508685 151891 532661 152398 311230 118386 765733 123253 852366 559739 409623 256380 662504 746040 817020 833978 322267 663353 316788 705688 003932 660075 517428 768045 / 4 > 3³²² [i]