MinT - Best Known (118, 118+47, s)-Nets in Base 8

Best Known (118, 118+47, s)-Nets in Base 8

(118, 118+47, 1026)-Net over F₈ — Constructive and digital

Digital (118, 165, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 165, 1026)-net over F₈, using
- 7 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]

(118, 118+47, 4484)-Net over F₈ — Digital

Digital (118, 165, 4484)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+47, 3704936)-Net in Base 8 — Upper bound on s

There is no (118, 165, 3704937)-net in base 8, because

1 times m-reduction [i] would yield (118, 164, 3704937)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12786 687143 947235 625439 212287 229630 963780 914447 602503 936377 022885 125462 035232 164051 366964 886380 350196 215391 270967 704232 368324 361146 348633 211816 936624 > 8¹⁶⁴ [i]