MinT - Best Known (161−119, 161, s)-Nets in Base 8

Best Known (161−119, 161, s)-Nets in Base 8

(161−119, 161, 98)-Net over F₈ — Constructive and digital

Digital (42, 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]

(161−119, 161, 129)-Net over F₈ — Digital

Digital (42, 161, 129)-net over F₈, using

t-expansion [i] based on digital (38, 161, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(161−119, 161, 879)-Net in Base 8 — Upper bound on s

There is no (42, 161, 880)-net in base 8, because

1 times m-reduction [i] would yield (42, 160, 880)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 146405 881302 152736 684609 894169 051004 488930 863328 030408 856311 042812 878009 854837 908736 340828 737466 910334 784942 363824 038368 850557 602214 344010 481292 > 8¹⁶⁰ [i]