MinT - Best Known (158−44, 158, s)-Nets in Base 8

Best Known (158−44, 158, s)-Nets in Base 8

(158−44, 158, 1026)-Net over F₈ — Constructive and digital

Digital (114, 158, 1026)-net over F₈, using

14 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 86, 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]

(158−44, 158, 5041)-Net over F₈ — Digital

Digital (114, 158, 5041)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−44, 158, 3958964)-Net in Base 8 — Upper bound on s

There is no (114, 158, 3958965)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48777 527658 623681 815197 258634 265839 250924 249034 199200 922972 252591 849900 246843 784311 768961 990852 734242 317690 304910 434990 071701 030665 442937 371504 > 8¹⁵⁸ [i]