MinT - Best Known (102, 153, s)-Nets in Base 8

Best Known (102, 153, s)-Nets in Base 8

(102, 153, 402)-Net over F₈ — Constructive and digital

Digital (102, 153, 402)-net over F₈, using

8¹ times duplication [i] based on digital (101, 152, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 36, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. digital (65, 116, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 58, 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]

(102, 153, 576)-Net in Base 8 — Constructive

(102, 153, 576)-net in base 8, using

9 times m-reduction [i] based on (102, 162, 576)-net in base 8, using
- trace code for nets [i] based on (21, 81, 288)-net in base 64, using
  - 3 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]

(102, 153, 1639)-Net over F₈ — Digital

Digital (102, 153, 1639)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 153, 450090)-Net in Base 8 — Upper bound on s

There is no (102, 153, 450091)-net in base 8, because

1 times m-reduction [i] would yield (102, 152, 450091)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186075 483669 740603 950781 052352 220905 434257 819409 725792 055415 728196 401186 355626 658665 060652 281221 713246 378456 664051 815178 561859 480480 717884 > 8¹⁵² [i]