MinT - Best Known (124−65, 124, s)-Nets in Base 8

Best Known (124−65, 124, s)-Nets in Base 8

(124−65, 124, 113)-Net over F₈ — Constructive and digital

Digital (59, 124, 113)-net over F₈, using

3 times m-reduction [i] based on digital (59, 127, 113)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 45, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. digital (14, 82, 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]

(124−65, 124, 171)-Net over F₈ — Digital

Digital (59, 124, 171)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−65, 124, 5387)-Net in Base 8 — Upper bound on s

There is no (59, 124, 5388)-net in base 8, because

1 times m-reduction [i] would yield (59, 123, 5388)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1202 996323 296603 284047 022179 224326 865047 188306 043915 337884 694949 768745 115471 039402 617601 683441 118268 292339 724792 > 8¹²³ [i]