MinT - Best Known (36, 36+109, s)-Nets in Base 8

Best Known (36, 36+109, s)-Nets in Base 8

(36, 36+109, 65)-Net over F₈ — Constructive and digital

Digital (36, 145, 65)-net over F₈, using

t-expansion [i] based on digital (14, 145, 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]

(36, 36+109, 112)-Net over F₈ — Digital

Digital (36, 145, 112)-net over F₈, using

t-expansion [i] based on digital (35, 145, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(36, 36+109, 733)-Net in Base 8 — Upper bound on s

There is no (36, 145, 734)-net in base 8, because

1 times m-reduction [i] would yield (36, 144, 734)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11862 073887 972419 923686 752284 796007 109043 185276 009262 113679 708232 866048 692677 139513 962573 517222 888611 491856 857559 103075 494324 264808 > 8¹⁴⁴ [i]