MinT - Best Known (63−31, 63, s)-Nets in Base 8

Best Known (63−31, 63, s)-Nets in Base 8

(63−31, 63, 130)-Net over F₈ — Constructive and digital

Digital (32, 63, 130)-net over F₈, using

1 times m-reduction [i] based on digital (32, 64, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 32, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(63−31, 63, 4950)-Net in Base 8 — Upper bound on s

There is no (32, 63, 4951)-net in base 8, because

1 times m-reduction [i] would yield (32, 62, 4951)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 259999 060598 637873 578783 080912 904727 113105 799607 290112 > 8⁶² [i]