MinT - Best Known (149−45, 149, s)-Nets in Base 8

Best Known (149−45, 149, s)-Nets in Base 8

(149−45, 149, 1026)-Net over F₈ — Constructive and digital

Digital (104, 149, 1026)-net over F₈, using

3 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]

(149−45, 149, 2840)-Net over F₈ — Digital

Digital (104, 149, 2840)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−45, 149, 1538451)-Net in Base 8 — Upper bound on s

There is no (104, 149, 1538452)-net in base 8, because

1 times m-reduction [i] would yield (104, 148, 1538452)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 427823 677352 357225 398141 140672 426780 991648 840183 162787 152064 850259 610626 019682 321715 371140 425249 661015 670542 983362 358648 739312 117536 > 8¹⁴⁸ [i]