MinT - Best Known (173−140, 173, s)-Nets in Base 8

Best Known (173−140, 173, s)-Nets in Base 8

(173−140, 173, 65)-Net over F₈ — Constructive and digital

Digital (33, 173, 65)-net over F₈, using

t-expansion [i] based on digital (14, 173, 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]

(173−140, 173, 97)-Net over F₈ — Digital

Digital (33, 173, 97)-net over F₈, using

t-expansion [i] based on digital (28, 173, 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]

(173−140, 173, 611)-Net in Base 8 — Upper bound on s

There is no (33, 173, 612)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 752915 498224 481649 631280 713040 520275 376139 579312 697823 991876 649447 957258 487070 339358 130548 445296 007760 338026 780828 544073 264773 286306 972280 746210 673638 174664 > 8¹⁷³ [i]