MinT - Best Known (57−55, 57, s)-Nets in Base 3

Best Known (57−55, 57, s)-Nets in Base 3

(57−55, 57, 8)-Net over F₃ — Constructive and digital

Digital (2, 57, 8)-net over F₃, using

net from sequence [i] based on digital (2, 7)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]

(57−55, 57, 9)-Net in Base 3 — Upper bound on s

There is no (2, 57, 10)-net in base 3, because

44 times m-reduction [i] would yield (2, 13, 10)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹³, 10, S₃, 3, 11), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 18 068994 / 11 > 3¹³ [i]