MinT - Best Known (111, 111+48, s)-Nets in Base 8

Best Known (111, 111+48, s)-Nets in Base 8

(111, 111+48, 1026)-Net over F₈ — Constructive and digital

Digital (111, 159, 1026)-net over F₈, using

7 times m-reduction [i] based on digital (111, 166, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 83, 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]

(111, 111+48, 3003)-Net over F₈ — Digital

Digital (111, 159, 3003)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+48, 1346576)-Net in Base 8 — Upper bound on s

There is no (111, 159, 1346577)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390221 736851 477720 416765 927146 448248 530149 679166 191792 270384 069067 117391 338206 139091 025625 318367 734107 506857 008043 603837 010214 342218 266608 580992 > 8¹⁵⁹ [i]