MinT - Best Known (166−46, 166, s)-Nets in Base 8

Best Known (166−46, 166, s)-Nets in Base 8

(166−46, 166, 1026)-Net over F₈ — Constructive and digital

Digital (120, 166, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 166, 1026)-net over F₈, using
- 6 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]

(166−46, 166, 5423)-Net over F₈ — Digital

Digital (120, 166, 5423)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−46, 166, 4439260)-Net in Base 8 — Upper bound on s

There is no (120, 166, 4439261)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818348 450664 091374 612816 374829 663082 591218 564314 498690 681315 309661 355446 978188 216005 714249 191000 441853 864774 247298 943511 479192 537684 405501 416730 961368 > 8¹⁶⁶ [i]