MinT - Best Known (152−45, 152, s)-Nets in Base 8

Best Known (152−45, 152, s)-Nets in Base 8

(152−45, 152, 1026)-Net over F₈ — Constructive and digital

Digital (107, 152, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (107, 158, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 79, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(152−45, 152, 3270)-Net over F₈ — Digital

Digital (107, 152, 3270)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−45, 152, 2042835)-Net in Base 8 — Upper bound on s

There is no (107, 152, 2042836)-net in base 8, because

1 times m-reduction [i] would yield (107, 151, 2042836)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23259 006173 932992 179117 621849 183064 579299 965070 436890 005972 382372 032906 955628 820252 370936 557782 440859 231115 105237 373065 673700 315968 138896 > 8¹⁵¹ [i]