MinT - Best Known (173−93, 173, s)-Nets in Base 8

Best Known (173−93, 173, s)-Nets in Base 8

(173−93, 173, 130)-Net over F₈ — Constructive and digital

Digital (80, 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)

(173−93, 173, 206)-Net over F₈ — Digital

Digital (80, 173, 206)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−93, 173, 6093)-Net in Base 8 — Upper bound on s

There is no (80, 173, 6094)-net in base 8, because

1 times m-reduction [i] would yield (80, 172, 6094)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 215969 492598 398014 316325 004388 918791 592477 971639 661234 744270 047775 200720 759687 971582 225414 003804 906325 290241 913833 065210 181088 104591 354533 749198 828697 411328 > 8¹⁷² [i]