MinT - Best Known (123−63, 123, s)-Nets in Base 8

Best Known (123−63, 123, s)-Nets in Base 8

(123−63, 123, 130)-Net over F₈ — Constructive and digital

Digital (60, 123, 130)-net over F₈, using

1 times m-reduction [i] based on digital (60, 124, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 46, 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, 78, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(123−63, 123, 187)-Net over F₈ — Digital

Digital (60, 123, 187)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−63, 123, 6334)-Net in Base 8 — Upper bound on s

There is no (60, 123, 6335)-net in base 8, because

1 times m-reduction [i] would yield (60, 122, 6335)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 150 782327 017782 908602 693670 823255 937063 262516 473884 956665 914364 390459 590189 249516 288506 474553 221820 428332 880520 > 8¹²² [i]