MinT - Best Known (112, 112+46, s)-Nets in Base 8

Best Known (112, 112+46, s)-Nets in Base 8

(112, 112+46, 1026)-Net over F₈ — Constructive and digital

Digital (112, 158, 1026)-net over F₈, using

10 times m-reduction [i] based on digital (112, 168, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 84, 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]

(112, 112+46, 3754)-Net over F₈ — Digital

Digital (112, 158, 3754)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+46, 2153728)-Net in Base 8 — Upper bound on s

There is no (112, 158, 2153729)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48777 667879 644172 917459 008562 770663 191537 983474 318723 867702 180432 919172 892426 636053 885497 585301 700546 524597 321057 556905 792216 717698 189203 278080 > 8¹⁵⁸ [i]