MinT - Best Known (127−34, 127, s)-Nets in Base 8

Best Known (127−34, 127, s)-Nets in Base 8

(127−34, 127, 1026)-Net over F₈ — Constructive and digital

Digital (93, 127, 1026)-net over F₈, using

3 times m-reduction [i] based on digital (93, 130, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 65, 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]

(127−34, 127, 5637)-Net over F₈ — Digital

Digital (93, 127, 5637)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−34, 127, 5720840)-Net in Base 8 — Upper bound on s

There is no (93, 127, 5720841)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 925264 312681 980419 450565 367405 379720 783555 622405 213976 599743 060566 908504 650879 262029 456217 411566 466173 595744 910080 > 8¹²⁷ [i]