MinT - Best Known (106, 151, s)-Nets in Base 8

Best Known (106, 151, s)-Nets in Base 8

(106, 151, 1026)-Net over F₈ — Constructive and digital

Digital (106, 151, 1026)-net over F₈, using

5 times m-reduction [i] based on digital (106, 156, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 78, 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]

(106, 151, 3120)-Net over F₈ — Digital

Digital (106, 151, 3120)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 151, 1858589)-Net in Base 8 — Upper bound on s

There is no (106, 151, 1858590)-net in base 8, because

1 times m-reduction [i] would yield (106, 150, 1858590)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2907 364855 842057 900746 985899 633837 702138 466881 320384 141832 096913 780372 457921 526954 235982 776561 133749 837168 778414 030179 351621 133040 018204 > 8¹⁵⁰ [i]