MinT - Best Known (13, 63, s)-Nets in Base 9

Best Known (13, 63, s)-Nets in Base 9

(13, 63, 64)-Net over F₉ — Constructive and digital

Digital (13, 63, 64)-net over F₉, using

net from sequence [i] based on digital (13, 63)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
  - a function field by GarcÃa and Quoos [i]

(13, 63, 298)-Net in Base 9 — Upper bound on s

There is no (13, 63, 299)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶³, 299, S₉, 50), but
- the linear programming bound shows that MÂ â‰¥ 10896 368310 901335 925878 885280 116060 856812 371650 402546 237637 731697 987582 281864 562263 286258 703283 319093 742959 047667 053474 566820 640625 / 8046 812733 958111 355218 192223 319952 526390 284250 015285 581584 155118 260761 > 9⁶³ [i]