MinT - Best Known (113, 113+55, s)-Nets in Base 8

Best Known (113, 113+55, s)-Nets in Base 8

(113, 113+55, 1026)-Net over F₈ — Constructive and digital

Digital (113, 168, 1026)-net over F₈, using

2 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]

(113, 113+55, 1959)-Net over F₈ — Digital

Digital (113, 168, 1959)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+55, 601278)-Net in Base 8 — Upper bound on s

There is no (113, 168, 601279)-net in base 8, because

1 times m-reduction [i] would yield (113, 167, 601279)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 547055 165035 548535 449307 856559 489545 295556 718275 049868 536615 121070 257398 102190 793687 973981 290827 322255 238254 417886 774860 705093 755884 236744 492960 721300 > 8¹⁶⁷ [i]