MinT - Best Known (149−52, 149, s)-Nets in Base 8

Best Known (149−52, 149, s)-Nets in Base 8

(149−52, 149, 382)-Net over F₈ — Constructive and digital

Digital (97, 149, 382)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (5, 31, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, 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]

(149−52, 149, 576)-Net in Base 8 — Constructive

(97, 149, 576)-net in base 8, using

5 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
- trace code for nets [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]

(149−52, 149, 1259)-Net over F₈ — Digital

Digital (97, 149, 1259)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−52, 149, 225716)-Net in Base 8 — Upper bound on s

There is no (97, 149, 225717)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 422744 030789 784872 146100 624019 617692 631527 341762 796431 296711 412638 972539 989568 111649 706833 773243 891190 173221 127330 280021 762523 523880 > 8¹⁴⁹ [i]