MinT - Best Known (63−54, 63, s)-Nets in Base 8

Best Known (63−54, 63, s)-Nets in Base 8

(63−54, 63, 45)-Net over F₈ — Constructive and digital

Digital (9, 63, 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]

(63−54, 63, 117)-Net in Base 8 — Upper bound on s

There is no (9, 63, 118)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶³, 118, S₈, 54), but
- the linear programming bound shows that MÂ â‰¥ 1276 877497 165858 550180 353268 717565 417447 419827 051453 679981 793142 090142 586954 518597 178383 779436 230367 997202 010049 204004 074370 891776 / 1 593132 553529 875882 064819 529430 499954 695292 500578 389894 815143 791958 969953 > 8⁶³ [i]