MinT - Best Known (59, 59+62, s)-Nets in Base 8

Best Known (59, 59+62, s)-Nets in Base 8

(59, 59+62, 130)-Net over F₈ — Constructive and digital

Digital (59, 121, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 45, 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, 76, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(59, 59+62, 184)-Net over F₈ — Digital

Digital (59, 121, 184)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+62, 5922)-Net in Base 8 — Upper bound on s

There is no (59, 121, 5923)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 873672 394104 262683 214850 208967 986455 231346 145574 615329 950495 297371 610869 996252 314522 996202 833611 191779 353440 > 8¹²¹ [i]