MinT - Best Known (34−25, 34, s)-Nets in Base 8

Best Known (34−25, 34, s)-Nets in Base 8

(34−25, 34, 45)-Net over F₈ — Constructive and digital

Digital (9, 34, 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]

(34−25, 34, 222)-Net in Base 8 — Upper bound on s

There is no (9, 34, 223)-net in base 8, because

1 times m-reduction [i] would yield (9, 33, 223)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 637969 240402 343041 807668 380657 > 8³³ [i]