MinT - Best Known (34−29, 34, s)-Nets in Base 9

Best Known (34−29, 34, s)-Nets in Base 9

(34−29, 34, 32)-Net over F₉ — Constructive and digital

Digital (5, 34, 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]

(34−29, 34, 120)-Net in Base 9 — Upper bound on s

There is no (5, 34, 121)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9³⁴, 121, S₉, 29), but
- the linear programming bound shows that MÂ â‰¥ 774 241071 394755 442550 540623 962575 701941 815040 879125 021541 / 2 775379 167034 318570 898365 > 9³⁴ [i]