MinT - Best Known (167−136, 167, s)-Nets in Base 8

Best Known (167−136, 167, s)-Nets in Base 8

(167−136, 167, 65)-Net over F₈ — Constructive and digital

Digital (31, 167, 65)-net over F₈, using

t-expansion [i] based on digital (14, 167, 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]

(167−136, 167, 97)-Net over F₈ — Digital

Digital (31, 167, 97)-net over F₈, using

t-expansion [i] based on digital (28, 167, 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]

(167−136, 167, 574)-Net in Base 8 — Upper bound on s

There is no (31, 167, 575)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 717194 869714 301824 493893 622296 420518 911630 882219 491912 334560 343736 088808 826172 629553 997184 890865 751372 009992 259809 924697 936745 933413 798502 455393 999912 > 8¹⁶⁷ [i]