MinT - Best Known (92, 92+60, s)-Nets in Base 8

Best Known (92, 92+60, s)-Nets in Base 8

(92, 92+60, 354)-Net over F₈ — Constructive and digital

Digital (92, 152, 354)-net over F₈, using

18 times m-reduction [i] based on digital (92, 170, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 85, 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]

(92, 92+60, 432)-Net in Base 8 — Constructive

(92, 152, 432)-net in base 8, using

trace code for nets [i] based on (16, 76, 216)-net in base 64, using
- 1 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 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]

(92, 92+60, 689)-Net over F₈ — Digital

Digital (92, 152, 689)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+60, 64747)-Net in Base 8 — Upper bound on s

There is no (92, 152, 64748)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186144 887733 001115 878316 525174 426738 516495 062317 915025 684127 237243 810753 127623 756727 304426 670053 389152 091369 425745 779266 107503 005049 345976 > 8¹⁵² [i]