MinT - Best Known (47, 47+45, s)-Nets in Base 8

Best Known (47, 47+45, s)-Nets in Base 8

(47, 47+45, 160)-Net over F₈ — Constructive and digital

Digital (47, 92, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 46, 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]

(47, 47+45, 179)-Net over F₈ — Digital

Digital (47, 92, 179)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+45, 7021)-Net in Base 8 — Upper bound on s

There is no (47, 92, 7022)-net in base 8, because

1 times m-reduction [i] would yield (47, 91, 7022)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15207 660841 221210 360934 732161 539200 973181 191597 311427 115380 330488 148046 379743 978216 > 8⁹¹ [i]