MinT - Best Known (171−156, 171, s)-Nets in Base 8

Best Known (171−156, 171, s)-Nets in Base 8

(171−156, 171, 65)-Net over F₈ — Constructive and digital

Digital (15, 171, 65)-net over F₈, using

t-expansion [i] based on digital (14, 171, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(171−156, 171, 122)-Net in Base 8 — Upper bound on s

There is no (15, 171, 123)-net in base 8, because

59 times m-reduction [i] would yield (15, 112, 123)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹¹², 123, S₈, 97), but
  - the linear programming bound shows that MÂ â‰¥ 753 868551 422368 025102 923082 320311 329646 383118 594947 491827 868209 928105 237207 212534 973299 462746 351662 301987 209216 / 4898 364625 > 8¹¹² [i]