MinT - Best Known (32, 32+108, s)-Nets in Base 8

Best Known (32, 32+108, s)-Nets in Base 8

(32, 32+108, 65)-Net over F₈ — Constructive and digital

Digital (32, 140, 65)-net over F₈, using

t-expansion [i] based on digital (14, 140, 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]

(32, 32+108, 97)-Net over F₈ — Digital

Digital (32, 140, 97)-net over F₈, using

t-expansion [i] based on digital (28, 140, 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]

(32, 32+108, 623)-Net in Base 8 — Upper bound on s

There is no (32, 140, 624)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 785967 348027 372626 763306 411550 657715 583122 087621 458221 595758 282778 039951 063350 859338 867599 771662 087720 238868 085604 203676 558948 > 8¹⁴⁰ [i]