MinT - Best Known (96, 96+66, s)-Nets in Base 8

Best Known (96, 96+66, s)-Nets in Base 8

(96, 96+66, 354)-Net over F₈ — Constructive and digital

Digital (96, 162, 354)-net over F₈, using

t-expansion [i] based on digital (93, 162, 354)-net over F₈, using
- 10 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+66, 384)-Net in Base 8 — Constructive

(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+66, 626)-Net over F₈ — Digital

Digital (96, 162, 626)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+66, 50983)-Net in Base 8 — Upper bound on s

There is no (96, 162, 50984)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 843229 630309 552430 160959 181744 666263 266899 668794 814198 070379 711062 879010 194820 340632 117284 137964 536217 437825 022621 437941 098461 133041 186913 206345 > 8¹⁶² [i]