MinT - Best Known (30−23, 30, s)-Nets in Base 8

Best Known (30−23, 30, s)-Nets in Base 8

(30−23, 30, 34)-Net over F₈ — Constructive and digital

Digital (7, 30, 34)-net over F₈, using

net from sequence [i] based on digital (7, 33)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(30−23, 30, 162)-Net in Base 8 — Upper bound on s

There is no (7, 30, 163)-net in base 8, because

1 times m-reduction [i] would yield (7, 29, 163)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 164 252095 142268 223699 262144 > 8²⁹ [i]