MinT - Best Known (59, 59+61, s)-Nets in Base 8

Best Known (59, 59+61, s)-Nets in Base 8

(59, 59+61, 130)-Net over F₈ — Constructive and digital

Digital (59, 120, 130)-net over F₈, using

1 times m-reduction [i] based on 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+61, 189)-Net over F₈ — Digital

Digital (59, 120, 189)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+61, 6557)-Net in Base 8 — Upper bound on s

There is no (59, 120, 6558)-net in base 8, because

1 times m-reduction [i] would yield (59, 119, 6558)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 294889 455957 186372 087272 226169 298820 503986 605400 981423 343466 452072 054157 515999 776560 491952 814965 071494 916880 > 8¹¹⁹ [i]