MinT - Best Known (124, 124+49, s)-Nets in Base 8

Best Known (124, 124+49, s)-Nets in Base 8

(124, 124+49, 1026)-Net over F₈ — Constructive and digital

Digital (124, 173, 1026)-net over F₈, using

8¹ times duplication [i] based on digital (123, 172, 1026)-net over F₈, using
- t-expansion [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(124, 124+49, 4839)-Net over F₈ — Digital

Digital (124, 173, 4839)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+49, 4153440)-Net in Base 8 — Upper bound on s

There is no (124, 173, 4153441)-net in base 8, because

1 times m-reduction [i] would yield (124, 172, 4153441)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214524 969561 971960 449626 852719 949686 407792 960903 879830 101679 947505 932762 592454 254389 594402 731293 641484 165181 248500 706984 318254 947702 473792 380980 696450 016708 > 8¹⁷² [i]