MinT - Best Known (146−52, 146, s)-Nets in Base 8

Best Known (146−52, 146, s)-Nets in Base 8

(146−52, 146, 371)-Net over F₈ — Constructive and digital

Digital (94, 146, 371)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (2, 28, 17)-net over F₈, using
  - net from sequence [i] based on digital (2, 16)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [i]
2. digital (66, 118, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 59, 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]

(146−52, 146, 576)-Net in Base 8 — Constructive

(94, 146, 576)-net in base 8, using

2 times m-reduction [i] based on (94, 148, 576)-net in base 8, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
  - 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 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]

(146−52, 146, 1117)-Net over F₈ — Digital

Digital (94, 146, 1117)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−52, 146, 177563)-Net in Base 8 — Upper bound on s

There is no (94, 146, 177564)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709886 558624 542588 944466 715976 523269 637558 953902 622716 509903 280215 417746 249479 748811 787854 407440 361845 659328 485064 311144 575100 120163 > 8¹⁴⁶ [i]