MinT - Best Known (102, 102+63, s)-Nets in Base 8

Best Known (102, 102+63, s)-Nets in Base 8

(102, 102+63, 354)-Net over F₈ — Constructive and digital

Digital (102, 165, 354)-net over F₈, using

t-expansion [i] based on digital (93, 165, 354)-net over F₈, using
- 7 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]

(102, 102+63, 432)-Net in Base 8 — Constructive

(102, 165, 432)-net in base 8, using

t-expansion [i] based on (101, 165, 432)-net in base 8, using
- 3 times m-reduction [i] based on (101, 168, 432)-net in base 8, using
  - trace code for nets [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]

(102, 102+63, 869)-Net over F₈ — Digital

Digital (102, 165, 869)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+63, 106290)-Net in Base 8 — Upper bound on s

There is no (102, 165, 106291)-net in base 8, because

1 times m-reduction [i] would yield (102, 164, 106291)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12789 962483 285748 201233 465676 326216 114879 371960 321821 779349 679292 905501 472386 877903 540694 600975 330539 721339 494375 227799 114778 360486 819346 456398 119840 > 8¹⁶⁴ [i]