MinT - Best Known (130−35, 130, s)-Nets in Base 8

Best Known (130−35, 130, s)-Nets in Base 8

(130−35, 130, 1026)-Net over F₈ — Constructive and digital

Digital (95, 130, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (95, 134, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 67, 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]

(130−35, 130, 5504)-Net over F₈ — Digital

Digital (95, 130, 5504)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−35, 130, 7306440)-Net in Base 8 — Upper bound on s

There is no (95, 130, 7306441)-net in base 8, because

1 times m-reduction [i] would yield (95, 129, 7306441)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 315 216317 834186 859388 655053 485338 702478 261102 592557 107199 648910 436448 937366 430846 755492 073375 717080 316834 726342 818240 > 8¹²⁹ [i]