MinT - Best Known (142−113, 142, s)-Nets in Base 8

Best Known (142−113, 142, s)-Nets in Base 8

(142−113, 142, 65)-Net over F₈ — Constructive and digital

Digital (29, 142, 65)-net over F₈, using

t-expansion [i] based on digital (14, 142, 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]

(142−113, 142, 97)-Net over F₈ — Digital

Digital (29, 142, 97)-net over F₈, using

t-expansion [i] based on digital (28, 142, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(142−113, 142, 547)-Net in Base 8 — Upper bound on s

There is no (29, 142, 548)-net in base 8, because

1 times m-reduction [i] would yield (29, 141, 548)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 143762 282624 705625 714149 522761 729519 992074 095641 221282 789676 843179 730050 859830 269812 157182 089608 134620 220364 628468 856266 552512 > 8¹⁴¹ [i]