MinT - Best Known (154−77, 154, s)-Nets in Base 8

Best Known (154−77, 154, s)-Nets in Base 8

(154−77, 154, 130)-Net over F₈ — Constructive and digital

Digital (77, 154, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 77, 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]

(154−77, 154, 249)-Net over F₈ — Digital

Digital (77, 154, 249)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−77, 154, 9262)-Net in Base 8 — Upper bound on s

There is no (77, 154, 9263)-net in base 8, because

1 times m-reduction [i] would yield (77, 153, 9263)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 493865 922753 702937 492935 007675 667725 845176 498237 725522 493065 071414 160124 320295 319636 859638 923253 221885 423970 797373 874615 678157 083380 480191 > 8¹⁵³ [i]