MinT - Best Known (73, 73+91, s)-Nets in Base 8

Best Known (73, 73+91, s)-Nets in Base 8

(73, 73+91, 130)-Net over F₈ — Constructive and digital

Digital (73, 164, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 59, 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, 105, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(73, 73+91, 174)-Net over F₈ — Digital

Digital (73, 164, 174)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+91, 4673)-Net in Base 8 — Upper bound on s

There is no (73, 164, 4674)-net in base 8, because

1 times m-reduction [i] would yield (73, 163, 4674)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1606 506342 701826 231848 561380 274060 395894 667493 011237 928265 207697 343555 503523 711615 503134 876911 279365 300779 257816 200915 346703 601282 122866 767318 061520 > 8¹⁶³ [i]