MinT - Best Known (25−17, 25, s)-Nets in Base 4

Best Known (25−17, 25, s)-Nets in Base 4

(25−17, 25, 21)-Net over F₄ — Constructive and digital

Digital (8, 25, 21)-net over F₄, using

t-expansion [i] based on digital (7, 25, 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]

(25−17, 25, 74)-Net in Base 4 — Upper bound on s

There is no (8, 25, 75)-net in base 4, because

1 times m-reduction [i] would yield (8, 24, 75)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 301 129767 026821 > 4²⁴ [i]