MinT - Best Known (155−123, 155, s)-Nets in Base 8

Best Known (155−123, 155, s)-Nets in Base 8

(155−123, 155, 65)-Net over F₈ — Constructive and digital

Digital (32, 155, 65)-net over F₈, using

t-expansion [i] based on digital (14, 155, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(155−123, 155, 97)-Net over F₈ — Digital

Digital (32, 155, 97)-net over F₈, using

t-expansion [i] based on digital (28, 155, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(155−123, 155, 603)-Net in Base 8 — Upper bound on s

There is no (32, 155, 604)-net in base 8, because

1 times m-reduction [i] would yield (32, 154, 604)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 768483 724154 292712 599935 639440 547955 394431 611467 626651 936891 723707 108409 802166 154069 554774 673220 499872 640519 024524 648892 193283 135361 624176 > 8¹⁵⁴ [i]