MinT - Best Known (157−50, 157, s)-Nets in Base 8

Best Known (157−50, 157, s)-Nets in Base 8

(157−50, 157, 1026)-Net over F₈ — Constructive and digital

Digital (107, 157, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (107, 158, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 79, 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]

(157−50, 157, 2161)-Net over F₈ — Digital

Digital (107, 157, 2161)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−50, 157, 682217)-Net in Base 8 — Upper bound on s

There is no (107, 157, 682218)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6097 228627 272088 633170 971753 691320 921124 386940 917724 608846 262120 950209 579242 279768 730899 673501 121904 399355 080415 721502 124204 480438 279632 208354 > 8¹⁵⁷ [i]