MinT - Best Known (15, 15+73, s)-Nets in Base 3

Best Known (15, 15+73, s)-Nets in Base 3

(15, 15+73, 28)-Net over F₃ — Constructive and digital

Digital (15, 88, 28)-net over F₃, 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+73, 42)-Net in Base 3 — Upper bound on s

There is no (15, 88, 43)-net in base 3, because

6 times m-reduction [i] would yield (15, 82, 43)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3⁸², 43, S₃, 2, 67), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 59862 575912 810098 943013 700133 585235 528405 / 34 > 3⁸² [i]