MinT - Best Known (22−18, 22, s)-Nets in Base 4

Best Known (22−18, 22, s)-Nets in Base 4

(22−18, 22, 15)-Net over F₄ — Constructive and digital

Digital (4, 22, 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]

(22−18, 22, 22)-Net in Base 4 — Upper bound on s

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

1 times m-reduction [i] would yield (4, 21, 23)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4²¹, 23, S₄, 2, 17), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 467529 936316 399616 / 88593 > 4²¹ [i]