MinT - Best Known (5, 39, s)-Nets in Base 9

Best Known (5, 39, s)-Nets in Base 9

(5, 39, 32)-Net over F₉ — Constructive and digital

Digital (5, 39, 32)-net over F₉, using

net from sequence [i] based on digital (5, 31)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
  - a function field by GarcÃa and Quoos [i]

(5, 39, 106)-Net in Base 9 — Upper bound on s

There is no (5, 39, 107)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9³⁹, 107, S₉, 34), but
- the linear programming bound shows that MÂ â‰¥ 6 494411 998936 567234 231022 707304 348082 650630 582149 950297 779220 585142 490175 / 378162 001389 969190 497317 361301 244231 > 9³⁹ [i]