MinT - Best Known (11, 11+50, s)-Nets in Base 8

Best Known (11, 11+50, s)-Nets in Base 8

(11, 11+50, 48)-Net over F₈ — Constructive and digital

Digital (11, 61, 48)-net over F₈, using

net from sequence [i] based on digital (11, 47)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
  - a function field by SÃ©mirat [i]

(11, 11+50, 190)-Net in Base 8 — Upper bound on s

There is no (11, 61, 191)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶¹, 191, S₈, 50), but
- the linear programming bound shows that MÂ â‰¥ 43 131717 252314 800123 297401 403184 511377 296444 354258 822923 969021 365663 939065 676566 961540 695380 950234 254636 162620 542890 499560 142906 640002 187264 / 3 448286 377926 195814 952375 837805 742664 085661 111547 354667 719069 757925 054643 462937 202051 > 8⁶¹ [i]