MinT - Best Known (100, 100+47, s)-Nets in Base 8

Best Known (100, 100+47, s)-Nets in Base 8

(100, 100+47, 419)-Net over F₈ — Constructive and digital

Digital (100, 147, 419)-net over F₈, using

1 times m-reduction [i] based on digital (100, 148, 419)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 38, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (62, 110, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 55, 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+47, 576)-Net in Base 8 — Constructive

(100, 147, 576)-net in base 8, using

11 times m-reduction [i] based on (100, 158, 576)-net in base 8, using
- trace code for nets [i] based on (21, 79, 288)-net in base 64, using
  - 5 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
    - base change [i] based on digital (9, 72, 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]

(100, 100+47, 2000)-Net over F₈ — Digital

Digital (100, 147, 2000)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+47, 727793)-Net in Base 8 — Upper bound on s

There is no (100, 147, 727794)-net in base 8, because

1 times m-reduction [i] would yield (100, 146, 727794)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709825 156740 750713 043367 775295 535579 161403 133884 451058 975892 800958 858299 171578 275622 297327 645625 041424 857007 528968 086054 502306 078800 > 8¹⁴⁶ [i]