MinT - Best Known (138−38, 138, s)-Nets in Base 8

Best Known (138−38, 138, s)-Nets in Base 8

(138−38, 138, 1026)-Net over F₈ — Constructive and digital

Digital (100, 138, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (100, 144, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 72, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(138−38, 138, 4906)-Net over F₈ — Digital

Digital (100, 138, 4906)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−38, 138, 4105834)-Net in Base 8 — Upper bound on s

There is no (100, 138, 4105835)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42307 760709 665985 914968 935039 735209 673532 114411 997759 309664 120148 473224 656467 374372 808929 096099 562724 700116 860201 188838 499296 > 8¹³⁸ [i]