MinT - Best Known (149−121, 149, s)-Nets in Base 8

Best Known (149−121, 149, s)-Nets in Base 8

(149−121, 149, 65)-Net over F₈ — Constructive and digital

Digital (28, 149, 65)-net over F₈, using

t-expansion [i] based on digital (14, 149, 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]

(149−121, 149, 97)-Net over F₈ — Digital

Digital (28, 149, 97)-net over F₈, using

net from sequence [i] based on digital (28, 96)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(149−121, 149, 522)-Net in Base 8 — Upper bound on s

There is no (28, 149, 523)-net in base 8, because

1 times m-reduction [i] would yield (28, 148, 523)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49 135102 275592 235344 950677 178652 376103 756352 804662 163469 004654 108729 587926 521044 766805 654042 738228 783687 896001 986856 869726 469952 034944 > 8¹⁴⁸ [i]