MinT - Best Known (154−56, 154, s)-Nets in Base 8

Best Known (154−56, 154, s)-Nets in Base 8

(154−56, 154, 363)-Net over F₈ — Constructive and digital

Digital (98, 154, 363)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 28, 9)-net over F₈, using
  - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
      - the rational function field F₈(x) [i]
    - Niederreiter sequence [i]
2. digital (70, 126, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 63, 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]

(154−56, 154, 576)-Net in Base 8 — Constructive

(98, 154, 576)-net in base 8, using

t-expansion [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]

(154−56, 154, 1054)-Net over F₈ — Digital

Digital (98, 154, 1054)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−56, 154, 149572)-Net in Base 8 — Upper bound on s

There is no (98, 154, 149573)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 910133 596282 509159 591115 147801 812493 450852 325033 777925 940955 473828 435139 841676 794903 427598 373902 814372 824567 311820 920318 219815 873535 365592 > 8¹⁵⁴ [i]