MinT - Best Known (57−48, 57, s)-Nets in Base 8

Best Known (57−48, 57, s)-Nets in Base 8

(57−48, 57, 45)-Net over F₈ — Constructive and digital

Digital (9, 57, 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]

(57−48, 57, 142)-Net in Base 8 — Upper bound on s

There is no (9, 57, 143)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁷, 143, S₈, 48), but
- the linear programming bound shows that MÂ â‰¥ 190 985064 753536 783415 540055 724940 511688 609267 854149 980012 811177 522699 203995 216683 345415 477517 845634 149018 525542 929152 325252 846051 935020 646400 / 62932 939565 275725 062929 480250 138238 153761 800884 105653 558972 374012 885252 408461 608921 201687 > 8⁵⁷ [i]