MinT - Best Known (108, 161, s)-Nets in Base 8

Best Known (108, 161, s)-Nets in Base 8

(108, 161, 513)-Net over F₈ — Constructive and digital

Digital (108, 161, 513)-net over F₈, using

base reduction for projective spaces (embedding PG(80,64) in PG(160,8)) for nets [i] based on digital (28, 81, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(108, 161, 576)-Net in Base 8 — Constructive

(108, 161, 576)-net in base 8, using

11 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
  - 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
    - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(108, 161, 1833)-Net over F₈ — Digital

Digital (108, 161, 1833)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 161, 544075)-Net in Base 8 — Upper bound on s

There is no (108, 161, 544076)-net in base 8, because

1 times m-reduction [i] would yield (108, 160, 544076)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 121873 539015 289207 608733 492418 970797 934220 351281 066308 734074 234950 280266 626350 930692 062335 453550 084325 347373 607783 927076 447808 186122 722847 382972 > 8¹⁶⁰ [i]