MinT - Best Known (96, 96+65, s)-Nets in Base 8

Best Known (96, 96+65, s)-Nets in Base 8

(96, 96+65, 354)-Net over F₈ — Constructive and digital

Digital (96, 161, 354)-net over F₈, using

t-expansion [i] based on digital (93, 161, 354)-net over F₈, using
- 11 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(96, 96+65, 384)-Net in Base 8 — Constructive

(96, 161, 384)-net in base 8, using

1 times m-reduction [i] based on (96, 162, 384)-net in base 8, using
- trace code for nets [i] based on (15, 81, 192)-net in base 64, using
  - 3 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(96, 96+65, 650)-Net over F₈ — Digital

Digital (96, 161, 650)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+65, 59853)-Net in Base 8 — Upper bound on s

There is no (96, 161, 59854)-net in base 8, because

1 times m-reduction [i] would yield (96, 160, 59854)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 123247 276474 615450 644176 939549 951930 917458 165692 802466 950852 537920 064400 876812 668719 960287 893142 804212 419492 817006 805341 585260 561035 874500 598626 > 8¹⁶⁰ [i]