MinT - Best Known (173−94, 173, s)-Nets in Base 8

Best Known (173−94, 173, s)-Nets in Base 8

(173−94, 173, 130)-Net over F₈ — Constructive and digital

Digital (79, 173, 130)-net over F₈, using

t-expansion [i] based on digital (76, 173, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 62, 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]
  2. digital (14, 111, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(173−94, 173, 198)-Net over F₈ — Digital

Digital (79, 173, 198)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−94, 173, 5505)-Net in Base 8 — Upper bound on s

There is no (79, 173, 5506)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 721568 219761 900229 406153 890005 638043 699059 853519 452768 095701 703679 848579 567387 681628 580762 782239 426995 883125 701710 902382 174986 267996 477276 088307 948910 263744 > 8¹⁷³ [i]