MinT - Best Known (45−36, 45, s)-Nets in Base 8

Best Known (45−36, 45, s)-Nets in Base 8

(45−36, 45, 45)-Net over F₈ — Constructive and digital

Digital (9, 45, 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]

(45−36, 45, 181)-Net in Base 8 — Upper bound on s

There is no (9, 45, 182)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁵, 182, S₈, 36), but
- the linear programming bound shows that MÂ â‰¥ 13756 503382 271877 018463 111544 707154 706642 586692 826474 347051 873971 078933 665018 818418 704384 / 299738 154218 773305 763010 805618 779690 296685 021501 > 8⁴⁵ [i]