MinT - Best Known (156−125, 156, s)-Nets in Base 8

Best Known (156−125, 156, s)-Nets in Base 8

(156−125, 156, 65)-Net over F₈ — Constructive and digital

Digital (31, 156, 65)-net over F₈, using

t-expansion [i] based on digital (14, 156, 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]

(156−125, 156, 97)-Net over F₈ — Digital

Digital (31, 156, 97)-net over F₈, using

t-expansion [i] based on digital (28, 156, 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]

(156−125, 156, 580)-Net in Base 8 — Upper bound on s

There is no (31, 156, 581)-net in base 8, because

1 times m-reduction [i] would yield (31, 155, 581)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102 319719 689773 770721 128610 935306 925365 080904 030999 653466 292645 557716 295007 512006 940184 851857 678338 923581 057544 108086 116260 049228 786364 014368 > 8¹⁵⁵ [i]