MinT - Best Known (27, 27+75, s)-Nets in Base 8

Best Known (27, 27+75, s)-Nets in Base 8

(27, 27+75, 65)-Net over F₈ — Constructive and digital

Digital (27, 102, 65)-net over F₈, using

t-expansion [i] based on digital (14, 102, 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]

(27, 27+75, 96)-Net over F₈ — Digital

Digital (27, 102, 96)-net over F₈, using

net from sequence [i] based on digital (27, 95)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 27 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(27, 27+75, 587)-Net in Base 8 — Upper bound on s

There is no (27, 102, 588)-net in base 8, because

1 times m-reduction [i] would yield (27, 101, 588)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 364664 213953 477506 995443 368903 204084 004865 745568 934244 946548 846459 395692 323904 081381 594156 > 8¹⁰¹ [i]