MinT - Best Known (162−49, 162, s)-Nets in Base 8

Best Known (162−49, 162, s)-Nets in Base 8

(162−49, 162, 1026)-Net over F₈ — Constructive and digital

Digital (113, 162, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (113, 170, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 85, 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]

(162−49, 162, 3014)-Net over F₈ — Digital

Digital (113, 162, 3014)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−49, 162, 1601361)-Net in Base 8 — Upper bound on s

There is no (113, 162, 1601362)-net in base 8, because

1 times m-reduction [i] would yield (113, 161, 1601362)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 974275 795854 117160 665013 243146 143448 660566 259666 568597 292396 976508 990624 121767 437332 176002 243726 834216 571885 051597 639537 747272 083678 988133 806088 > 8¹⁶¹ [i]