MinT - Best Known (123−61, 123, s)-Nets in Base 8

Best Known (123−61, 123, s)-Nets in Base 8

(123−61, 123, 130)-Net over F₈ — Constructive and digital

Digital (62, 123, 130)-net over F₈, using

1 times m-reduction [i] based on digital (62, 124, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 62, 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]

(123−61, 123, 213)-Net over F₈ — Digital

Digital (62, 123, 213)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−61, 123, 8076)-Net in Base 8 — Upper bound on s

There is no (62, 123, 8077)-net in base 8, because

1 times m-reduction [i] would yield (62, 122, 8077)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 150 324481 324323 980959 003283 036516 991420 711299 902651 168131 392513 367156 844085 918017 264336 125097 504701 962716 034112 > 8¹²² [i]