MinT - Best Known (2, 2+13, s)-Nets in Base 4

Best Known (2, 2+13, s)-Nets in Base 4

(2, 2+13, 10)-Net over F₄ — Constructive and digital

Digital (2, 15, 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+13, 13)-Net in Base 4 — Upper bound on s

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

extracting embedded OOA [i] would yield OOA(4¹⁵, 14, S₄, 2, 13), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 55834 574848 / 47 > 4¹⁵ [i]