MinT - Best Known (89−84, 89, s)-Nets in Base 4

Best Known (89−84, 89, s)-Nets in Base 4

(89−84, 89, 17)-Net over F₄ — Constructive and digital

Digital (5, 89, 17)-net over F₄, using

net from sequence [i] based on digital (5, 16)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]

(89−84, 89, 23)-Net in Base 4 — Upper bound on s

There is no (5, 89, 24)-net in base 4, because

58 times m-reduction [i] would yield (5, 31, 24)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4³¹, 24, S₄, 2, 26), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 5 737162 226617 068887 736320 / 1 225547 > 4³¹ [i]