MinT - Best Known (18, 18+92, s)-Nets in Base 7

Best Known (18, 18+92, s)-Nets in Base 7

(18, 18+92, 26)-Net over F₇ — Constructive and digital

Digital (18, 110, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(18, 18+92, 51)-Net over F₇ — Digital

Digital (18, 110, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(18, 18+92, 130)-Net in Base 7 — Upper bound on s

There is no (18, 110, 131)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹¹⁰, 131, S₇, 92), but
- the linear programming bound shows that MÂ â‰¥ 14844 021583 061281 810785 857957 798057 986038 448447 732466 281611 485140 339675 903295 997408 057152 892923 374510 382776 095703 / 15 529811 970796 784375 > 7¹¹⁰ [i]