MinT - Best Known (150−55, 150, s)-Nets in Base 8

Best Known (150−55, 150, s)-Nets in Base 8

(150−55, 150, 354)-Net over F₈ — Constructive and digital

Digital (95, 150, 354)-net over F₈, using

t-expansion [i] based on digital (93, 150, 354)-net over F₈, using
- 22 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]

(150−55, 150, 576)-Net in Base 8 — Constructive

(95, 150, 576)-net in base 8, using

trace code for nets [i] based on (20, 75, 288)-net in base 64, using
- 2 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]

(150−55, 150, 988)-Net over F₈ — Digital

Digital (95, 150, 988)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−55, 150, 150306)-Net in Base 8 — Upper bound on s

There is no (95, 150, 150307)-net in base 8, because

1 times m-reduction [i] would yield (95, 149, 150307)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 427539 784616 678575 499073 451411 901923 068978 053385 706431 496605 819321 601156 598956 059028 860469 101753 022072 060967 540894 515437 239112 463872 > 8¹⁴⁹ [i]