MinT - Best Known (9, 9+35, s)-Nets in Base 8

Best Known (9, 9+35, s)-Nets in Base 8

(9, 9+35, 45)-Net over F₈ — Constructive and digital

Digital (9, 44, 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]

(9, 9+35, 186)-Net in Base 8 — Upper bound on s

There is no (9, 44, 187)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁴, 187, S₈, 35), but
- the linear programming bound shows that MÂ â‰¥ 627920 235018 576761 086030 356765 156624 937089 584240 096441 720995 357774 692087 280294 690816 / 109 868250 399981 715090 671787 569185 054383 324443 > 8⁴⁴ [i]