MinT - Best Known (13, 64, s)-Nets in Base 9

Best Known (13, 64, s)-Nets in Base 9

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

Digital (13, 64, 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, 64, 292)-Net in Base 9 — Upper bound on s

There is no (13, 64, 293)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁴, 293, S₉, 51), but
- the linear programming bound shows that MÂ â‰¥ 47 002307 922196 063905 160210 696113 610328 519723 893737 703695 883154 769019 296625 870089 104049 534698 268889 554450 926349 442513 951738 579830 462540 000000 / 3 925469 228422 809712 472549 701705 794999 500528 495643 205441 129825 846296 957998 796349 > 9⁶⁴ [i]