MinT - Best Known (30−21, 30, s)-Nets in Base 8

Best Known (30−21, 30, s)-Nets in Base 8

(30−21, 30, 45)-Net over F₈ — Constructive and digital

Digital (9, 30, 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]

(30−21, 30, 263)-Net in Base 8 — Upper bound on s

There is no (9, 30, 264)-net in base 8, because

1 times m-reduction [i] would yield (9, 29, 264)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 159 598001 431025 515707 712672 > 8²⁹ [i]