MinT - Best Known (20−13, 20, s)-Nets in Base 4

Best Known (20−13, 20, s)-Nets in Base 4

(20−13, 20, 21)-Net over F₄ — Constructive and digital

Digital (7, 20, 21)-net over F₄, using

net from sequence [i] based on digital (7, 20)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
  - an explicitly constructive algebraic function field [i]

(20−13, 20, 76)-Net in Base 4 — Upper bound on s

There is no (7, 20, 77)-net in base 4, because

1 times m-reduction [i] would yield (7, 19, 77)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 294588 977068 > 4¹⁹ [i]