MinT - Best Known (111, 111+47, s)-Nets in Base 8

Best Known (111, 111+47, s)-Nets in Base 8

(111, 111+47, 1026)-Net over F₈ — Constructive and digital

Digital (111, 158, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (111, 166, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 83, 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]

(111, 111+47, 3274)-Net over F₈ — Digital

Digital (111, 158, 3274)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+47, 1967550)-Net in Base 8 — Upper bound on s

There is no (111, 158, 1967551)-net in base 8, because

1 times m-reduction [i] would yield (111, 157, 1967551)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6097 207540 474590 139990 544058 447261 102072 505649 025998 183298 076668 399005 427362 050570 941923 855281 812935 064379 189988 582777 869422 870179 704270 188832 > 8¹⁵⁷ [i]