MinT - Best Known (152−56, 152, s)-Nets in Base 8

Best Known (152−56, 152, s)-Nets in Base 8

(152−56, 152, 354)-Net over F₈ — Constructive and digital

Digital (96, 152, 354)-net over F₈, using

t-expansion [i] based on digital (93, 152, 354)-net over F₈, using
- 20 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(152−56, 152, 576)-Net in Base 8 — Constructive

(96, 152, 576)-net in base 8, using

trace code for nets [i] based on (20, 76, 288)-net in base 64, using
- 1 times m-reduction [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]

(152−56, 152, 974)-Net over F₈ — Digital

Digital (96, 152, 974)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−56, 152, 128924)-Net in Base 8 — Upper bound on s

There is no (96, 152, 128925)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186077 835091 790679 775400 056155 940057 534618 081559 336853 847980 361275 668020 816388 460740 122419 324918 637270 623230 061386 518180 675019 215245 084825 > 8¹⁵² [i]