MinT - Best Known (81−57, 81, s)-Nets in Base 8

Best Known (81−57, 81, s)-Nets in Base 8

(81−57, 81, 65)-Net over F₈ — Constructive and digital

Digital (24, 81, 65)-net over F₈, using

t-expansion [i] based on digital (14, 81, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(81−57, 81, 81)-Net over F₈ — Digital

Digital (24, 81, 81)-net over F₈, using

net from sequence [i] based on digital (24, 80)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 24 and N(F) ≥ 81, using
  - a curve from the manYPoints database [i]

(81−57, 81, 596)-Net in Base 8 — Upper bound on s

There is no (24, 81, 597)-net in base 8, because

1 times m-reduction [i] would yield (24, 80, 597)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 795614 786838 093173 234089 423380 226470 436082 813813 225605 919866 164743 192984 > 8⁸⁰ [i]