MinT - Best Known (161−51, 161, s)-Nets in Base 8

Best Known (161−51, 161, s)-Nets in Base 8

(161−51, 161, 1026)-Net over F₈ — Constructive and digital

Digital (110, 161, 1026)-net over F₈, using

3 times m-reduction [i] based on digital (110, 164, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 82, 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]

(161−51, 161, 2277)-Net over F₈ — Digital

Digital (110, 161, 2277)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−51, 161, 875580)-Net in Base 8 — Upper bound on s

There is no (110, 161, 875581)-net in base 8, because

1 times m-reduction [i] would yield (110, 160, 875581)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 121811 159813 019967 535329 227679 733092 971400 158200 617567 220875 246775 018540 827210 611351 412155 918633 536232 256732 973388 682914 753495 649261 779660 159044 > 8¹⁶⁰ [i]