MinT - Best Known (45−36, 45, s)-Nets in Base 7

Best Known (45−36, 45, s)-Nets in Base 7

(45−36, 45, 17)-Net over F₇ — Constructive and digital

Digital (9, 45, 17)-net over F₇, using

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

(45−36, 45, 38)-Net over F₇ — Digital

Digital (9, 45, 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]

(45−36, 45, 144)-Net in Base 7 — Upper bound on s

There is no (9, 45, 145)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁵, 145, S₇, 36), but
- the linear programming bound shows that MÂ â‰¥ 1 813054 297468 894563 118987 208872 174502 813939 418289 052616 398499 773838 510369 693534 865836 965625 / 16446 905309 677963 308897 231434 343903 438067 922584 484783 > 7⁴⁵ [i]