MinT - Best Known (173−53, 173, s)-Nets in Base 8

Best Known (173−53, 173, s)-Nets in Base 8

(173−53, 173, 1026)-Net over F₈ — Constructive and digital

Digital (120, 173, 1026)-net over F₈, using

8¹ times duplication [i] based on digital (119, 172, 1026)-net over F₈, using
- t-expansion [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]

(173−53, 173, 2945)-Net over F₈ — Digital

Digital (120, 173, 2945)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−53, 173, 1420619)-Net in Base 8 — Upper bound on s

There is no (120, 173, 1420620)-net in base 8, because

1 times m-reduction [i] would yield (120, 172, 1420620)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214528 466273 028776 285844 460250 701783 189160 321305 618280 367934 321035 159470 115388 542518 294718 376009 860701 214270 667748 286054 894863 953347 614413 000933 898706 100156 > 8¹⁷² [i]