MinT - Best Known (64, 64+36, s)-Nets in Base 8

Best Known (64, 64+36, s)-Nets in Base 8

(64, 64+36, 354)-Net over F₈ — Constructive and digital

Digital (64, 100, 354)-net over F₈, using

14 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+36, 516)-Net in Base 8 — Constructive

(64, 100, 516)-net in base 8, using

base change [i] based on digital (39, 75, 516)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (39, 76, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 38, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(64, 64+36, 773)-Net over F₈ — Digital

Digital (64, 100, 773)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+36, 112242)-Net in Base 8 — Upper bound on s

There is no (64, 100, 112243)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 037330 594859 744773 109626 262844 480703 628690 047765 212818 643541 532776 314499 909449 116073 945275 > 8¹⁰⁰ [i]