MinT - Best Known (142−110, 142, s)-Nets in Base 8

Best Known (142−110, 142, s)-Nets in Base 8

(142−110, 142, 65)-Net over F₈ — Constructive and digital

Digital (32, 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]

(142−110, 142, 97)-Net over F₈ — Digital

Digital (32, 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]

(142−110, 142, 619)-Net in Base 8 — Upper bound on s

There is no (32, 142, 620)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 175 659781 736401 132273 574999 586563 749197 840553 093949 654068 738784 697686 687983 089216 335617 086608 474887 295360 175623 327664 207321 044424 > 8¹⁴² [i]