MinT - Best Known (161−117, 161, s)-Nets in Base 8

Best Known (161−117, 161, s)-Nets in Base 8

(161−117, 161, 98)-Net over F₈ — Constructive and digital

Digital (44, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(161−117, 161, 130)-Net over F₈ — Digital

Digital (44, 161, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(161−117, 161, 957)-Net in Base 8 — Upper bound on s

There is no (44, 161, 958)-net in base 8, because

1 times m-reduction [i] would yield (44, 160, 958)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 180871 214784 546729 320994 191571 316544 225662 105354 905948 778702 146662 366633 772587 379755 987056 030889 380890 858727 221258 977061 443176 544958 042746 004270 > 8¹⁶⁰ [i]