MinT - Best Known (119−102, 119, s)-Nets in Base 8

Best Known (119−102, 119, s)-Nets in Base 8

(119−102, 119, 65)-Net over F₈ — Constructive and digital

Digital (17, 119, 65)-net over F₈, using

t-expansion [i] based on digital (14, 119, 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]

(119−102, 119, 138)-Net in Base 8 — Upper bound on s

There is no (17, 119, 139)-net in base 8, because

1 times m-reduction [i] would yield (17, 118, 139)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹¹⁸, 139, S₈, 101), but
  - the linear programming bound shows that MÂ â‰¥ 86 122166 823419 594361 457243 405645 198855 851117 431259 906299 815036 071096 967116 729798 784443 354837 373006 252286 343831 710016 130244 411392 / 2218 870601 774953 928217 > 8¹¹⁸ [i]