MinT - Best Known (155−59, 155, s)-Nets in Base 8

Best Known (155−59, 155, s)-Nets in Base 8

(155−59, 155, 354)-Net over F₈ — Constructive and digital

Digital (96, 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]

(155−59, 155, 432)-Net in Base 8 — Constructive

(96, 155, 432)-net in base 8, using

3 times m-reduction [i] based on (96, 158, 432)-net in base 8, using
- trace code for nets [i] based on (17, 79, 216)-net in base 64, using
  - 5 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
    - base change [i] based on digital (5, 72, 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]

(155−59, 155, 837)-Net over F₈ — Digital

Digital (96, 155, 837)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−59, 155, 104151)-Net in Base 8 — Upper bound on s

There is no (96, 155, 104152)-net in base 8, because

1 times m-reduction [i] would yield (96, 154, 104152)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 908546 458115 692703 666625 468232 202890 886766 587267 333690 370583 684167 933525 526801 953314 699302 632731 474184 264362 622980 241178 951789 685161 859960 > 8¹⁵⁴ [i]