MinT - Best Known (84, 84+50, s)-Nets in Base 8

Best Known (84, 84+50, s)-Nets in Base 8

(84, 84+50, 354)-Net over F₈ — Constructive and digital

Digital (84, 134, 354)-net over F₈, using

20 times m-reduction [i] based on digital (84, 154, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 77, 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]

(84, 84+50, 514)-Net in Base 8 — Constructive

(84, 134, 514)-net in base 8, using

trace code for nets [i] based on (17, 67, 257)-net in base 64, using
- 1 times m-reduction [i] based on (17, 68, 257)-net in base 64, using
  - base change [i] based on digital (0, 51, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]

(84, 84+50, 825)-Net over F₈ — Digital

Digital (84, 134, 825)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+50, 100698)-Net in Base 8 — Upper bound on s

There is no (84, 134, 100699)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 330300 778455 093473 277705 549350 530236 453067 870705 113787 321216 784801 342914 238996 893354 268944 997029 779367 196745 184089 867222 > 8¹³⁴ [i]