MinT - Best Known (13, 13+89, s)-Nets in Base 9

Best Known (13, 13+89, s)-Nets in Base 9

(13, 13+89, 64)-Net over F₉ — Constructive and digital

Digital (13, 102, 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, 13+89, 130)-Net in Base 9 — Upper bound on s

There is no (13, 102, 131)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9¹⁰², 131, S₉, 89), but
- the linear programming bound shows that MÂ â‰¥ 5084 374080 189706 177359 309140 360076 786478 181531 648392 793018 884753 216582 007355 917174 929352 796335 303716 584419 612836 913783 114175 / 226 109038 131612 894412 430848 > 9¹⁰² [i]