MinT - Best Known (70, 137, s)-Nets in Base 8

Best Known (70, 137, s)-Nets in Base 8

(70, 137, 160)-Net over F₈ — Constructive and digital

Digital (70, 137, 160)-net over F₈, using

1 times m-reduction [i] based on digital (70, 138, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 69, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(70, 137, 247)-Net over F₈ — Digital

Digital (70, 137, 247)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 137, 9889)-Net in Base 8 — Upper bound on s

There is no (70, 137, 9890)-net in base 8, because

1 times m-reduction [i] would yield (70, 136, 9890)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 662 207369 206975 718888 026374 833061 633110 203672 678274 674232 980426 113362 123174 066600 451940 555157 077786 339855 763775 052332 855251 > 8¹³⁶ [i]