MinT - Best Known (104−52, 104, s)-Nets in Base 8

Best Known (104−52, 104, s)-Nets in Base 8

(104−52, 104, 130)-Net over F₈ — Constructive and digital

Digital (52, 104, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 52, 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]

(104−52, 104, 180)-Net over F₈ — Digital

Digital (52, 104, 180)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−52, 104, 6157)-Net in Base 8 — Upper bound on s

There is no (52, 104, 6158)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8356 610242 046914 708126 022118 834029 377244 762507 763516 064617 167742 205996 840769 221122 287235 134720 > 8¹⁰⁴ [i]