MinT - Best Known (50−41, 50, s)-Nets in Base 8

Best Known (50−41, 50, s)-Nets in Base 8

(50−41, 50, 45)-Net over F₈ — Constructive and digital

Digital (9, 50, 45)-net over F₈, using

net from sequence [i] based on digital (9, 44)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]

(50−41, 50, 167)-Net in Base 8 — Upper bound on s

There is no (9, 50, 168)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁰, 168, S₈, 41), but
- the linear programming bound shows that MÂ â‰¥ 88 878925 675468 594252 545475 672766 298360 795865 099885 627226 789704 425844 909316 598387 436637 913725 787396 322099 200000 / 60401 155569 972260 736537 739420 987860 179092 086900 861398 054688 001507 > 8⁵⁰ [i]