MinT - Best Known (170−46, 170, s)-Nets in Base 8

Best Known (170−46, 170, s)-Nets in Base 8

(170−46, 170, 1026)-Net over F₈ — Constructive and digital

Digital (124, 170, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 170, 1026)-net over F₈, using
- 2 times m-reduction [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]

(170−46, 170, 6520)-Net over F₈ — Digital

Digital (124, 170, 6520)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−46, 170, 6373385)-Net in Base 8 — Upper bound on s

There is no (124, 170, 6373386)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3351 953523 155040 036595 980163 879701 547471 527748 210663 303547 036417 802912 998234 821678 093099 286521 014323 680396 054011 258177 134182 171447 770198 548402 790935 891968 > 8¹⁷⁰ [i]