MinT - Best Known (2, 2+12, s)-Nets in Base 4

Best Known (2, 2+12, s)-Nets in Base 4

(2, 2+12, 10)-Net over F₄ — Constructive and digital

Digital (2, 14, 10)-net over F₄, using

net from sequence [i] based on digital (2, 9)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]

(2, 2+12, 14)-Net in Base 4 — Upper bound on s

There is no (2, 14, 15)-net in base 4, because

1 times m-reduction [i] would yield (2, 13, 15)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4¹³, 15, S₄, 2, 11), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 7113 539584 / 103 > 4¹³ [i]