MinT - Best Known (55−52, 55, s)-Nets in Base 3

Best Known (55−52, 55, s)-Nets in Base 3

(55−52, 55, 10)-Net over F₃ — Constructive and digital

Digital (3, 55, 10)-net over F₃, using

net from sequence [i] based on digital (3, 9)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]

(55−52, 55, 11)-Net in Base 3 — Upper bound on s

There is no (3, 55, 12)-net in base 3, because

33 times m-reduction [i] would yield (3, 22, 12)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²², 12, S₃, 3, 19), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 28 839193 780671 / 895 > 3²² [i]