MinT - Best Known (104, 147, s)-Nets in Base 8

Best Known (104, 147, s)-Nets in Base 8

(104, 147, 1026)-Net over F₈ — Constructive and digital

Digital (104, 147, 1026)-net over F₈, using

5 times m-reduction [i] based on digital (104, 152, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 76, 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]

(104, 147, 3437)-Net over F₈ — Digital

Digital (104, 147, 3437)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 147, 2355145)-Net in Base 8 — Upper bound on s

There is no (104, 147, 2355146)-net in base 8, because

1 times m-reduction [i] would yield (104, 146, 2355146)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709806 228991 357384 474389 734222 828894 449353 488654 665350 645495 498352 182437 247336 533702 277065 458089 936450 059722 641225 727069 608848 461448 > 8¹⁴⁶ [i]