MinT - Best Known (45−38, 45, s)-Nets in Base 8

Best Known (45−38, 45, s)-Nets in Base 8

(45−38, 45, 34)-Net over F₈ — Constructive and digital

Digital (7, 45, 34)-net over F₈, using

net from sequence [i] based on digital (7, 33)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(45−38, 45, 125)-Net in Base 8 — Upper bound on s

There is no (7, 45, 126)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁵, 126, S₈, 38), but
- the linear programming bound shows that MÂ â‰¥ 97 988261 153178 759183 515307 564235 965998 809450 008822 438931 431923 006231 411365 301452 800000 / 2231 099651 930719 207985 256014 175260 370353 497421 > 8⁴⁵ [i]