MinT - Best Known (13−9, 13, s)-Nets in Base 4

Best Known (13−9, 13, s)-Nets in Base 4

(13−9, 13, 15)-Net over F₄ — Constructive and digital

Digital (4, 13, 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]

(13−9, 13, 44)-Net in Base 4 — Upper bound on s

There is no (4, 13, 45)-net in base 4, because

1 times m-reduction [i] would yield (4, 12, 45)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 17 568631 > 4¹² [i]