MinT - Best Known (153−47, 153, s)-Nets in Base 8

Best Known (153−47, 153, s)-Nets in Base 8

(153−47, 153, 1026)-Net over F₈ — Constructive and digital

Digital (106, 153, 1026)-net over F₈, using

3 times m-reduction [i] based on digital (106, 156, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 78, 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]

(153−47, 153, 2616)-Net over F₈ — Digital

Digital (106, 153, 2616)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−47, 153, 1251987)-Net in Base 8 — Upper bound on s

There is no (106, 153, 1251988)-net in base 8, because

1 times m-reduction [i] would yield (106, 152, 1251988)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186070 828585 321334 702035 771753 100327 743208 755410 127441 997327 365442 953438 307503 095774 849947 469095 283823 067828 182632 277229 032628 935917 108064 > 8¹⁵² [i]