MinT - Best Known (110−95, 110, s)-Nets in Base 8

Best Known (110−95, 110, s)-Nets in Base 8

(110−95, 110, 65)-Net over F₈ — Constructive and digital

Digital (15, 110, 65)-net over F₈, using

t-expansion [i] based on digital (14, 110, 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]

(110−95, 110, 123)-Net in Base 8 — Upper bound on s

There is no (15, 110, 124)-net in base 8, because

2 times m-reduction [i] would yield (15, 108, 124)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹⁰⁸, 124, S₈, 93), but
  - the linear programming bound shows that MÂ â‰¥ 302067 636843 505531 883890 845707 740199 346768 359063 955658 182923 822512 167902 446126 353225 119662 763164 078853 468429 746176 / 7795 981619 009375 > 8¹⁰⁸ [i]