MinT - Best Known (100, 100+67, s)-Nets in Base 8

Best Known (100, 100+67, s)-Nets in Base 8

(100, 100+67, 354)-Net over F₈ — Constructive and digital

Digital (100, 167, 354)-net over F₈, using

t-expansion [i] based on digital (93, 167, 354)-net over F₈, using
- 5 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]

(100, 100+67, 384)-Net in Base 8 — Constructive

(100, 167, 384)-net in base 8, using

t-expansion [i] based on (99, 167, 384)-net in base 8, using
- 1 times m-reduction [i] based on (99, 168, 384)-net in base 8, using
  - trace code for nets [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(100, 100+67, 690)-Net over F₈ — Digital

Digital (100, 167, 690)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+67, 65604)-Net in Base 8 — Upper bound on s

There is no (100, 167, 65605)-net in base 8, because

1 times m-reduction [i] would yield (100, 166, 65605)-net in base 8, but
- 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]