MinT - Best Known (65−22, 65, s)-Nets in Base 8

Best Known (65−22, 65, s)-Nets in Base 8

(65−22, 65, 354)-Net over F₈ — Constructive and digital

Digital (43, 65, 354)-net over F₈, using

7 times m-reduction [i] based on digital (43, 72, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 36, 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]

(65−22, 65, 518)-Net in Base 8 — Constructive

(43, 65, 518)-net in base 8, using

8¹ times duplication [i] based on (42, 64, 518)-net in base 8, using
- base change [i] based on digital (26, 48, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 24, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(65−22, 65, 784)-Net over F₈ — Digital

Digital (43, 65, 784)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−22, 65, 152173)-Net in Base 8 — Upper bound on s

There is no (43, 65, 152174)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 50219 690853 310226 560088 047420 188532 869456 802122 327190 127914 > 8⁶⁵ [i]