MinT - Best Known (89−76, 89, s)-Nets in Base 8

Best Known (89−76, 89, s)-Nets in Base 8

(89−76, 89, 48)-Net over F₈ — Constructive and digital

Digital (13, 89, 48)-net over F₈, using

t-expansion [i] based on digital (11, 89, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(89−76, 89, 56)-Net over F₈ — Digital

Digital (13, 89, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(89−76, 89, 133)-Net in Base 8 — Upper bound on s

There is no (13, 89, 134)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸⁹, 134, S₈, 76), but
- the linear programming bound shows that MÂ â‰¥ 339 564876 213791 903441 446701 624147 319546 654476 560183 972243 504035 566505 332528 890424 541850 326383 262283 223839 644030 328124 184335 131828 795470 043523 579904 / 1 403647 453766 705048 417279 815383 471540 207854 050620 481255 363553 906325 > 8⁸⁹ [i]