MinT - Best Known (154−124, 154, s)-Nets in Base 8

Best Known (154−124, 154, s)-Nets in Base 8

(154−124, 154, 65)-Net over F₈ — Constructive and digital

Digital (30, 154, 65)-net over F₈, using

t-expansion [i] based on digital (14, 154, 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]

(154−124, 154, 97)-Net over F₈ — Digital

Digital (30, 154, 97)-net over F₈, using

t-expansion [i] based on digital (28, 154, 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]

(154−124, 154, 559)-Net in Base 8 — Upper bound on s

There is no (30, 154, 560)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 034395 315206 877567 303196 562420 714574 480427 798682 615707 094249 541839 866855 356680 719221 882786 382349 920468 411300 861894 574494 607737 622633 688992 > 8¹⁵⁴ [i]