MinT - Best Known (9, 20, s)-Nets in Base 8

Best Known (9, 20, s)-Nets in Base 8

(9, 20, 45)-Net over F₈ — Constructive and digital

Digital (9, 20, 45)-net over F₈, using

net from sequence [i] based on digital (9, 44)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]

(9, 20, 1003)-Net in Base 8 — Upper bound on s

There is no (9, 20, 1004)-net in base 8, because

1 times m-reduction [i] would yield (9, 19, 1004)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 144821 978100 659658 > 8¹⁹ [i]