MinT - Best Known (31−22, 31, s)-Nets in Base 8

Best Known (31−22, 31, s)-Nets in Base 8

(31−22, 31, 45)-Net over F₈ — Constructive and digital

Digital (9, 31, 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]

(31−22, 31, 239)-Net in Base 8 — Upper bound on s

There is no (9, 31, 240)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10120 569717 937540 016951 340007 > 8³¹ [i]