MinT - Best Known (111−95, 111, s)-Nets in Base 8

Best Known (111−95, 111, s)-Nets in Base 8

(111−95, 111, 65)-Net over F₈ — Constructive and digital

Digital (16, 111, 65)-net over F₈, using

t-expansion [i] based on digital (14, 111, 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]

(111−95, 111, 133)-Net in Base 8 — Upper bound on s

There is no (16, 111, 134)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8¹¹¹, 134, S₈, 95), but
- the linear programming bound shows that MÂ â‰¥ 3213 718744 248367 464211 966828 793200 685277 723323 269317 408810 044111 174024 201867 677763 903619 161246 026196 671187 301423 896682 561536 / 165729 471662 280587 916075 > 8¹¹¹ [i]