MinT - Best Known (166−62, 166, s)-Nets in Base 8

Best Known (166−62, 166, s)-Nets in Base 8

(166−62, 166, 354)-Net over F₈ — Constructive and digital

Digital (104, 166, 354)-net over F₈, using

t-expansion [i] based on digital (93, 166, 354)-net over F₈, using
- 6 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(166−62, 166, 576)-Net in Base 8 — Constructive

(104, 166, 576)-net in base 8, using

trace code for nets [i] based on (21, 83, 288)-net in base 64, using
- 1 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
  - base change [i] based on digital (9, 72, 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]

(166−62, 166, 975)-Net over F₈ — Digital

Digital (104, 166, 975)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−62, 166, 121553)-Net in Base 8 — Upper bound on s

There is no (104, 166, 121554)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818494 888410 763245 521783 527028 942474 483825 841262 029404 280164 045590 267768 788960 472393 882419 173941 768466 059959 013927 687320 535987 903868 527164 570575 170464 > 8¹⁶⁶ [i]