MinT - Best Known (133−109, 133, s)-Nets in Base 8

Best Known (133−109, 133, s)-Nets in Base 8

(133−109, 133, 65)-Net over F₈ — Constructive and digital

Digital (24, 133, 65)-net over F₈, using

t-expansion [i] based on digital (14, 133, 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]

(133−109, 133, 81)-Net over F₈ — Digital

Digital (24, 133, 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]

(133−109, 133, 449)-Net in Base 8 — Upper bound on s

There is no (24, 133, 450)-net in base 8, because

1 times m-reduction [i] would yield (24, 132, 450)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 169599 892375 309647 697041 061177 451620 867487 688716 455154 494608 099505 216565 733763 962988 737405 906828 318886 784529 137994 600032 > 8¹³² [i]