MinT - Best Known (97, 97+39, s)-Nets in Base 8

Best Known (97, 97+39, s)-Nets in Base 8

(97, 97+39, 1026)-Net over F₈ — Constructive and digital

Digital (97, 136, 1026)-net over F₈, using

2 times m-reduction [i] based on digital (97, 138, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 69, 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]

(97, 97+39, 3682)-Net over F₈ — Digital

Digital (97, 136, 3682)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+39, 2956703)-Net in Base 8 — Upper bound on s

There is no (97, 136, 2956704)-net in base 8, because

1 times m-reduction [i] would yield (97, 135, 2956704)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 632322 473691 326950 223732 783214 657785 144061 850314 537994 247273 683795 220188 801832 648642 223009 330763 158420 758352 466142 541931 > 8¹³⁵ [i]