MinT - Best Known (166−68, 166, s)-Nets in Base 8

Best Known (166−68, 166, s)-Nets in Base 8

(166−68, 166, 354)-Net over F₈ — Constructive and digital

Digital (98, 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]

(166−68, 166, 384)-Net in Base 8 — Constructive

(98, 166, 384)-net in base 8, using

trace code for nets [i] based on (15, 83, 192)-net in base 64, using
- 1 times m-reduction [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]

(166−68, 166, 623)-Net over F₈ — Digital

Digital (98, 166, 623)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−68, 166, 49590)-Net in Base 8 — Upper bound on s

There is no (98, 166, 49591)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818885 545758 591758 249108 909138 662541 357316 725506 969464 665503 748492 544320 324950 677383 313341 229526 073571 174045 146286 324655 738059 253881 013051 913789 696581 > 8¹⁶⁶ [i]