MinT - Best Known (49−40, 49, s)-Nets in Base 8

Best Known (49−40, 49, s)-Nets in Base 8

(49−40, 49, 45)-Net over F₈ — Constructive and digital

Digital (9, 49, 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]

(49−40, 49, 170)-Net in Base 8 — Upper bound on s

There is no (9, 49, 171)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁹, 171, S₈, 40), but
- the linear programming bound shows that MÂ â‰¥ 4 934719 031057 018522 247066 188340 383610 023541 755640 637271 866087 507054 558638 954604 396734 723391 488000 / 26766 851870 989741 605277 523047 483360 506612 498376 936729 > 8⁴⁹ [i]