MinT - Best Known (28, 28+133, s)-Nets in Base 8

Best Known (28, 28+133, s)-Nets in Base 8

(28, 28+133, 65)-Net over F₈ — Constructive and digital

Digital (28, 161, 65)-net over F₈, using

t-expansion [i] based on digital (14, 161, 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]

(28, 28+133, 97)-Net over F₈ — Digital

Digital (28, 161, 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]

(28, 28+133, 520)-Net in Base 8 — Upper bound on s

There is no (28, 161, 521)-net in base 8, because

1 times m-reduction [i] would yield (28, 160, 521)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 340089 343956 085896 664432 024953 150544 461235 087391 430981 147158 129160 982701 351114 805407 100036 987591 113759 648003 956549 923790 275768 450088 221077 850912 > 8¹⁶⁰ [i]