MinT - Best Known (79, 79+78, s)-Nets in Base 8

Best Known (79, 79+78, s)-Nets in Base 8

(79, 79+78, 130)-Net over F₈ — Constructive and digital

Digital (79, 157, 130)-net over F₈, using

1 times m-reduction [i] based on digital (79, 158, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 79, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(79, 79+78, 260)-Net over F₈ — Digital

Digital (79, 157, 260)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+78, 9478)-Net in Base 8 — Upper bound on s

There is no (79, 157, 9479)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6120 555522 582850 546567 225557 145912 428991 043908 154019 385383 412256 970401 111256 211556 600885 526255 765336 393186 456857 850372 504842 558690 242945 443392 > 8¹⁵⁷ [i]