MinT - Best Known (166−134, 166, s)-Nets in Base 8

Best Known (166−134, 166, s)-Nets in Base 8

(166−134, 166, 65)-Net over F₈ — Constructive and digital

Digital (32, 166, 65)-net over F₈, using

t-expansion [i] based on digital (14, 166, 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]

(166−134, 166, 97)-Net over F₈ — Digital

Digital (32, 166, 97)-net over F₈, using

t-expansion [i] based on digital (28, 166, 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]

(166−134, 166, 594)-Net in Base 8 — Upper bound on s

There is no (32, 166, 595)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 841043 215851 815920 198003 113120 107997 872515 507742 297754 027216 454655 304953 884727 888073 136145 264717 555388 404214 153953 863654 325782 733411 385911 619191 492680 > 8¹⁶⁶ [i]