MinT - Best Known (158−122, 158, s)-Nets in Base 8

Best Known (158−122, 158, s)-Nets in Base 8

(158−122, 158, 65)-Net over F₈ — Constructive and digital

Digital (36, 158, 65)-net over F₈, using

t-expansion [i] based on digital (14, 158, 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]

(158−122, 158, 112)-Net over F₈ — Digital

Digital (36, 158, 112)-net over F₈, using

t-expansion [i] based on digital (35, 158, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(158−122, 158, 696)-Net in Base 8 — Upper bound on s

There is no (36, 158, 697)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49315 154030 424870 058486 232300 163750 816776 859482 518136 974220 461801 015242 405169 844874 652309 140154 516126 066354 070955 451232 333932 675976 353970 318720 > 8¹⁵⁸ [i]