MinT - Best Known (168−48, 168, s)-Nets in Base 8

Best Known (168−48, 168, s)-Nets in Base 8

(168−48, 168, 1026)-Net over F₈ — Constructive and digital

Digital (120, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(168−48, 168, 4460)-Net over F₈ — Digital

Digital (120, 168, 4460)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−48, 168, 2936921)-Net in Base 8 — Upper bound on s

There is no (120, 168, 2936922)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 374292 720229 785730 545653 263157 837963 143024 153762 495046 307466 740522 184033 867483 389791 147961 464630 597641 438421 257995 928407 227272 037206 042637 572246 289197 > 8¹⁶⁸ [i]