MinT - Best Known (144−40, 144, s)-Nets in Base 8

Best Known (144−40, 144, s)-Nets in Base 8

(144−40, 144, 1026)-Net over F₈ — Constructive and digital

Digital (104, 144, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (104, 152, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 76, 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]

(144−40, 144, 4771)-Net over F₈ — Digital

Digital (104, 144, 4771)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−40, 144, 3770983)-Net in Base 8 — Upper bound on s

There is no (104, 144, 3770984)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11090 686792 968889 262220 610871 560373 293025 686578 646021 468746 654210 779483 218983 107260 310075 788038 790504 857495 256182 703565 249109 426782 > 8¹⁴⁴ [i]