MinT - Best Known (12, 12+72, s)-Nets in Base 8

Best Known (12, 12+72, s)-Nets in Base 8

(12, 12+72, 48)-Net over F₈ — Constructive and digital

Digital (12, 84, 48)-net over F₈, using

t-expansion [i] based on digital (11, 84, 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+72, 49)-Net over F₈ — Digital

Digital (12, 84, 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+72, 121)-Net in Base 8 — Upper bound on s

There is no (12, 84, 122)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸⁴, 122, S₈, 72), but
- the linear programming bound shows that MÂ â‰¥ 13 667710 905790 957223 957926 820133 087109 743318 931481 072391 569344 280694 781095 929058 079413 218689 209468 031544 701421 178025 148416 / 1833 598385 597924 151286 636785 201918 120213 797655 > 8⁸⁴ [i]