MinT - Best Known (155−61, 155, s)-Nets in Base 8

Best Known (155−61, 155, s)-Nets in Base 8

(155−61, 155, 354)-Net over F₈ — Constructive and digital

Digital (94, 155, 354)-net over F₈, using

t-expansion [i] based on digital (93, 155, 354)-net over F₈, using
- 17 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]

(155−61, 155, 432)-Net in Base 8 — Constructive

(94, 155, 432)-net in base 8, using

8¹ times duplication [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]

(155−61, 155, 711)-Net over F₈ — Digital

Digital (94, 155, 711)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−61, 155, 74377)-Net in Base 8 — Upper bound on s

There is no (94, 155, 74378)-net in base 8, because

1 times m-reduction [i] would yield (94, 154, 74378)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 909843 170876 169106 049844 428633 189095 001347 525299 144702 017718 720670 485342 263917 387528 685967 491746 158762 256816 437417 779952 463314 846502 706624 > 8¹⁵⁴ [i]