MinT - Best Known (64, 64+34, s)-Nets in Base 8

Best Known (64, 64+34, s)-Nets in Base 8

(64, 64+34, 354)-Net over F₈ — Constructive and digital

Digital (64, 98, 354)-net over F₈, using

16 times m-reduction [i] based on digital (64, 114, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 57, 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]

(64, 64+34, 518)-Net in Base 8 — Constructive

(64, 98, 518)-net in base 8, using

8² times duplication [i] based on (62, 96, 518)-net in base 8, using
- base change [i] based on digital (38, 72, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(64, 64+34, 920)-Net over F₈ — Digital

Digital (64, 98, 920)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+34, 164766)-Net in Base 8 — Upper bound on s

There is no (64, 98, 164767)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31831 669449 038937 104815 799176 783621 708373 449641 948942 925088 128249 183869 116242 045220 924910 > 8⁹⁸ [i]