MinT - Best Known (5, 18, s)-Nets in Base 4

Best Known (5, 18, s)-Nets in Base 4

(5, 18, 17)-Net over F₄ — Constructive and digital

Digital (5, 18, 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]

(5, 18, 46)-Net in Base 4 — Upper bound on s

There is no (5, 18, 47)-net in base 4, because

1 times m-reduction [i] would yield (5, 17, 47)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18556 207147 > 4¹⁷ [i]