MinT - Best Known (157−129, 157, s)-Nets in Base 8

Best Known (157−129, 157, s)-Nets in Base 8

(157−129, 157, 65)-Net over F₈ — Constructive and digital

Digital (28, 157, 65)-net over F₈, using

t-expansion [i] based on digital (14, 157, 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]

(157−129, 157, 97)-Net over F₈ — Digital

Digital (28, 157, 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]

(157−129, 157, 520)-Net in Base 8 — Upper bound on s

There is no (28, 157, 521)-net in base 8, because

1 times m-reduction [i] would yield (28, 156, 521)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 804 392381 156446 614651 858709 105926 706233 006335 132817 776845 978582 190109 364028 597663 198195 161651 249416 123888 090742 956704 645292 925933 655093 054904 > 8¹⁵⁶ [i]