MinT - Best Known (102, 156, s)-Nets in Base 8

Best Known (102, 156, s)-Nets in Base 8

(102, 156, 388)-Net over F₈ — Constructive and digital

Digital (102, 156, 388)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 34, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (68, 122, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 61, 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, 156, 576)-Net in Base 8 — Constructive

(102, 156, 576)-net in base 8, using

6 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, 156, 1366)-Net over F₈ — Digital

Digital (102, 156, 1366)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 156, 257711)-Net in Base 8 — Upper bound on s

There is no (102, 156, 257712)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 195830 367744 950382 262539 001782 773400 646972 450351 586250 709131 273005 513075 045647 310287 000363 049861 485982 729677 393530 951694 470150 349322 349654 > 8¹⁵⁶ [i]