MinT - Best Known (138−135, 138, s)-Nets in Base 4

Best Known (138−135, 138, s)-Nets in Base 4

(138−135, 138, 14)-Net over F₄ — Constructive and digital

Digital (3, 138, 14)-net over F₄, using

net from sequence [i] based on digital (3, 13)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]

(138−135, 138, 16)-Net in Base 4 — Upper bound on s

There is no (3, 138, 17)-net in base 4, because

118 times m-reduction [i] would yield (3, 20, 17)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4²⁰, 17, S₄, 2, 17), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 3 573412 790272 / 3 > 4²⁰ [i]