MinT - Best Known (83−41, 83, s)-Nets in Base 8

Best Known (83−41, 83, s)-Nets in Base 8

(83−41, 83, 130)-Net over F₈ — Constructive and digital

Digital (42, 83, 130)-net over F₈, using

1 times m-reduction [i] based on digital (42, 84, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 42, 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]

(83−41, 83, 158)-Net over F₈ — Digital

Digital (42, 83, 158)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−41, 83, 5970)-Net in Base 8 — Upper bound on s

There is no (42, 83, 5971)-net in base 8, because

1 times m-reduction [i] would yield (42, 82, 5971)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 428753 898064 645620 544001 343831 378360 459004 880666 716359 240127 586277 429776 > 8⁸² [i]