MinT - Best Known (166−66, 166, s)-Nets in Base 8

Best Known (166−66, 166, s)-Nets in Base 8

(166−66, 166, 354)-Net over F₈ — Constructive and digital

Digital (100, 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]

(166−66, 166, 432)-Net in Base 8 — Constructive

(100, 166, 432)-net in base 8, using

trace code for nets [i] based on (17, 83, 216)-net in base 64, using
- 1 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
  - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(166−66, 166, 717)-Net over F₈ — Digital

Digital (100, 166, 717)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−66, 166, 65604)-Net in Base 8 — Upper bound on s

There is no (100, 166, 65605)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818450 895373 297146 354468 879813 605332 915213 229960 830599 991238 516070 712266 997055 618190 983289 261371 227973 387416 698981 408316 044661 011641 940344 927105 827928 > 8¹⁶⁶ [i]