MinT - Best Known (63−50, 63, s)-Nets in Base 8

Best Known (63−50, 63, s)-Nets in Base 8

(63−50, 63, 48)-Net over F₈ — Constructive and digital

Digital (13, 63, 48)-net over F₈, using

t-expansion [i] based on digital (11, 63, 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]

(63−50, 63, 56)-Net over F₈ — Digital

Digital (13, 63, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(63−50, 63, 245)-Net in Base 8 — Upper bound on s

There is no (13, 63, 246)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶³, 246, S₈, 50), but
- the linear programming bound shows that MÂ â‰¥ 72 840298 861777 373992 611187 558191 542500 874164 967824 087893 687769 883750 796155 293411 965734 562225 167841 125941 095948 685567 759789 000438 579200 / 90458 637942 667222 659888 243669 560729 928842 753977 381226 885636 066397 611640 849491 > 8⁶³ [i]