MinT - Best Known (47−38, 47, s)-Nets in Base 7

Best Known (47−38, 47, s)-Nets in Base 7

(47−38, 47, 17)-Net over F₇ — Constructive and digital

Digital (9, 47, 17)-net over F₇, using

net from sequence [i] based on digital (9, 16)-sequence over F₇, using
- Niederreiter sequence [i]

(47−38, 47, 38)-Net over F₇ — Digital

Digital (9, 47, 38)-net over F₇, using

net from sequence [i] based on digital (9, 37)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
  - an algebraic function field over â„¤₇ by Yeo [i]

(47−38, 47, 140)-Net in Base 7 — Upper bound on s

There is no (9, 47, 141)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁷, 141, S₇, 38), but
- the linear programming bound shows that MÂ â‰¥ 7 042926 790555 044156 510932 458331 124543 458315 183458 738161 153908 191601 065071 940274 711993 814455 953125 / 1209 642061 001961 603577 647550 110669 284554 662415 208194 445083 > 7⁴⁷ [i]