MinT - Best Known (143−39, 143, s)-Nets in Base 8

Best Known (143−39, 143, s)-Nets in Base 8

(143−39, 143, 1026)-Net over F₈ — Constructive and digital

Digital (104, 143, 1026)-net over F₈, using

9 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]

(143−39, 143, 5391)-Net over F₈ — Digital

Digital (104, 143, 5391)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−39, 143, 6361009)-Net in Base 8 — Upper bound on s

There is no (104, 143, 6361010)-net in base 8, because

1 times m-reduction [i] would yield (104, 142, 6361010)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 292123 318051 305259 826842 748316 813538 097052 128743 931980 318577 807908 104074 745498 161258 173147 276246 225577 697687 905821 412422 998736 > 8¹⁴² [i]