MinT - Best Known (108, 166, s)-Nets in Base 8

Best Known (108, 166, s)-Nets in Base 8

(108, 166, 388)-Net over F₈ — Constructive and digital

Digital (108, 166, 388)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 36, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (72, 130, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 65, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(108, 166, 576)-Net in Base 8 — Constructive

(108, 166, 576)-net in base 8, using

6 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
  - 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
    - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(108, 166, 1374)-Net over F₈ — Digital

Digital (108, 166, 1374)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 166, 246265)-Net in Base 8 — Upper bound on s

There is no (108, 166, 246266)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818392 012635 297565 813147 823330 924757 659278 637245 956415 458537 360300 764716 307810 115999 754149 671192 462648 607912 587330 103234 022909 947240 910436 915220 180088 > 8¹⁶⁶ [i]