MinT - Best Known (153−59, 153, s)-Nets in Base 8

Best Known (153−59, 153, s)-Nets in Base 8

(153−59, 153, 354)-Net over F₈ — Constructive and digital

Digital (94, 153, 354)-net over F₈, using

t-expansion [i] based on digital (93, 153, 354)-net over F₈, using
- 19 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]

(153−59, 153, 432)-Net in Base 8 — Constructive

(94, 153, 432)-net in base 8, using

t-expansion [i] based on (93, 153, 432)-net in base 8, using
- 1 times m-reduction [i] based on (93, 154, 432)-net in base 8, using
  - trace code for nets [i] based on (16, 77, 216)-net in base 64, using
    - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(153−59, 153, 777)-Net over F₈ — Digital

Digital (94, 153, 777)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−59, 153, 90234)-Net in Base 8 — Upper bound on s

There is no (94, 153, 90235)-net in base 8, because

1 times m-reduction [i] would yield (94, 152, 90235)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186085 217222 681371 828066 248505 401789 199303 505743 570046 465014 386257 143516 780231 138697 823826 249289 814530 825690 111987 487493 409774 640597 917936 > 8¹⁵² [i]