MinT - Best Known (165−133, 165, s)-Nets in Base 8

Best Known (165−133, 165, s)-Nets in Base 8

(165−133, 165, 65)-Net over F₈ — Constructive and digital

Digital (32, 165, 65)-net over F₈, using

t-expansion [i] based on digital (14, 165, 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]

(165−133, 165, 97)-Net over F₈ — Digital

Digital (32, 165, 97)-net over F₈, using

t-expansion [i] based on digital (28, 165, 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]

(165−133, 165, 595)-Net in Base 8 — Upper bound on s

There is no (32, 165, 596)-net in base 8, because

1 times m-reduction [i] would yield (32, 164, 596)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13153 389342 703100 512398 099360 790916 787138 490066 176018 091847 936232 714670 370166 315222 626752 190638 375622 567019 920969 396828 114490 925118 486503 995460 963991 > 8¹⁶⁴ [i]