MinT - Best Known (12, 12+70, s)-Nets in Base 8

Best Known (12, 12+70, s)-Nets in Base 8

(12, 12+70, 48)-Net over F₈ — Constructive and digital

Digital (12, 82, 48)-net over F₈, using

t-expansion [i] based on digital (11, 82, 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]

(12, 12+70, 49)-Net over F₈ — Digital

Digital (12, 82, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(12, 12+70, 133)-Net in Base 8 — Upper bound on s

There is no (12, 82, 134)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸², 134, S₈, 70), but
- the linear programming bound shows that MÂ â‰¥ 4664 792125 777722 046138 669484 580667 923762 109664 287813 372039 061403 950327 295683 944068 621540 722857 216067 407381 242172 440982 210176 081265 832424 404034 781184 / 40 907897 444591 418153 695678 067428 562685 685978 075503 783565 710042 297338 389277 > 8⁸² [i]