MinT - Best Known (168−136, 168, s)-Nets in Base 8

Best Known (168−136, 168, s)-Nets in Base 8

(168−136, 168, 65)-Net over F₈ — Constructive and digital

Digital (32, 168, 65)-net over F₈, using

t-expansion [i] based on digital (14, 168, 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]

(168−136, 168, 97)-Net over F₈ — Digital

Digital (32, 168, 97)-net over F₈, using

t-expansion [i] based on digital (28, 168, 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]

(168−136, 168, 593)-Net in Base 8 — Upper bound on s

There is no (32, 168, 594)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 919413 598233 347114 340634 812646 786741 175881 460361 323965 601168 062884 532764 640618 030036 839428 851576 564950 964207 100446 736078 944242 551013 060200 853019 889340 > 8¹⁶⁸ [i]