MinT - Best Known (163−134, 163, s)-Nets in Base 8

Best Known (163−134, 163, s)-Nets in Base 8

(163−134, 163, 65)-Net over F₈ — Constructive and digital

Digital (29, 163, 65)-net over F₈, using

t-expansion [i] based on digital (14, 163, 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]

(163−134, 163, 97)-Net over F₈ — Digital

Digital (29, 163, 97)-net over F₈, using

t-expansion [i] based on digital (28, 163, 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]

(163−134, 163, 538)-Net in Base 8 — Upper bound on s

There is no (29, 163, 539)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1746 511536 695523 017025 660836 426173 657494 723255 917678 773965 283058 278432 176286 606351 828718 627571 999146 549541 776979 144166 768120 585611 025673 289458 431872 > 8¹⁶³ [i]