MinT - Best Known (173−90, 173, s)-Nets in Base 8

Best Known (173−90, 173, s)-Nets in Base 8

(173−90, 173, 130)-Net over F₈ — Constructive and digital

Digital (83, 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)

(173−90, 173, 236)-Net over F₈ — Digital

Digital (83, 173, 236)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−90, 173, 7435)-Net in Base 8 — Upper bound on s

There is no (83, 173, 7436)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 723293 695649 691901 807533 891748 888534 023345 459405 346275 035455 821755 611089 092045 759440 790016 762036 395226 241277 036450 594353 655819 269046 833392 491469 693193 989568 > 8¹⁷³ [i]