MinT - Best Known (12−10, 12, s)-Nets in Base 3

Best Known (12−10, 12, s)-Nets in Base 3

(12−10, 12, 8)-Net over F₃ — Constructive and digital

Digital (2, 12, 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]

(12−10, 12, 10)-Net in Base 3 — Upper bound on s

There is no (2, 12, 11)-net in base 3, because

extracting embedded OOA [i] would yield OOA(3¹², 11, S₃, 2, 10), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 200 884698 / 331 > 3¹² [i]