MinT - Best Known (48−39, 48, s)-Nets in Base 8

Best Known (48−39, 48, s)-Nets in Base 8

(48−39, 48, 45)-Net over F₈ — Constructive and digital

Digital (9, 48, 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]

(48−39, 48, 172)-Net in Base 8 — Upper bound on s

There is no (9, 48, 173)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁸, 173, S₈, 39), but
- the linear programming bound shows that MÂ â‰¥ 126 296880 587848 998506 683320 646458 767835 732888 608563 089124 509881 267958 927414 601530 963292 135096 320000 / 5 163225 106518 531786 586828 445312 912503 027015 263681 020423 > 8⁴⁸ [i]