MinT - Best Known (35−30, 35, s)-Nets in Base 9

Best Known (35−30, 35, s)-Nets in Base 9

(35−30, 35, 32)-Net over F₉ — Constructive and digital

Digital (5, 35, 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]

(35−30, 35, 118)-Net in Base 9 — Upper bound on s

There is no (5, 35, 119)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9³⁵, 119, S₉, 30), but
- the linear programming bound shows that MÂ â‰¥ 1099 290304 855686 981588 611152 801901 132646 862736 773934 593125 / 437133 003325 626637 437277 > 9³⁵ [i]