MinT - Best Known (161−73, 161, s)-Nets in Base 8

Best Known (161−73, 161, s)-Nets in Base 8

(161−73, 161, 354)-Net over F₈ — Constructive and digital

Digital (88, 161, 354)-net over F₈, using

1 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(161−73, 161, 390)-Net over F₈ — Digital

Digital (88, 161, 390)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−73, 161, 21033)-Net in Base 8 — Upper bound on s

There is no (88, 161, 21034)-net in base 8, because

1 times m-reduction [i] would yield (88, 160, 21034)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 126061 256348 431801 092393 563674 000096 199242 197019 453712 437999 333114 002947 508307 577071 199030 146128 828763 377608 474823 713871 532798 694653 965232 259510 > 8¹⁶⁰ [i]