MinT - Best Known (4, 4+19, s)-Nets in Base 4

Best Known (4, 4+19, s)-Nets in Base 4

(4, 4+19, 15)-Net over F₄ — Constructive and digital

Digital (4, 23, 15)-net over F₄, using

net from sequence [i] based on digital (4, 14)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
  - an explicitly constructive algebraic function field [i]

(4, 4+19, 21)-Net in Base 4 — Upper bound on s

There is no (4, 23, 22)-net in base 4, because

extracting embedded OOA [i] would yield OOA(4²³, 22, S₄, 2, 19), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 13 473010 866488 082432 / 165637 > 4²³ [i]