MinT - Best Known (173−51, 173, s)-Nets in Base 8

Best Known (173−51, 173, s)-Nets in Base 8

(173−51, 173, 1026)-Net over F₈ — Constructive and digital

Digital (122, 173, 1026)-net over F₈, using

8¹ times duplication [i] based on digital (121, 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]

(173−51, 173, 3734)-Net over F₈ — Digital

Digital (122, 173, 3734)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−51, 173, 2375658)-Net in Base 8 — Upper bound on s

There is no (122, 173, 2375659)-net in base 8, because

1 times m-reduction [i] would yield (122, 172, 2375659)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214525 562746 372392 083773 727852 978993 636309 187684 099297 812134 018183 076832 182431 537553 916668 459852 664490 639853 342964 039442 456614 803755 850847 458114 714113 559620 > 8¹⁷² [i]