MinT - Best Known (173−144, 173, s)-Nets in Base 8

Best Known (173−144, 173, s)-Nets in Base 8

(173−144, 173, 65)-Net over F₈ — Constructive and digital

Digital (29, 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]

(173−144, 173, 97)-Net over F₈ — Digital

Digital (29, 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]

(173−144, 173, 538)-Net in Base 8 — Upper bound on s

There is no (29, 173, 539)-net in base 8, because

2 times m-reduction [i] would yield (29, 171, 539)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27612 665833 549641 006533 351851 416393 268585 620641 291558 469114 614550 962312 020008 963561 232180 218725 078182 170242 890980 487371 179742 729493 583911 971922 580395 024576 > 8¹⁷¹ [i]