MinT - Best Known (136−101, 136, s)-Nets in Base 8

Best Known (136−101, 136, s)-Nets in Base 8

(136−101, 136, 65)-Net over F₈ — Constructive and digital

Digital (35, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 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]

(136−101, 136, 112)-Net over F₈ — Digital

Digital (35, 136, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(136−101, 136, 732)-Net in Base 8 — Upper bound on s

There is no (35, 136, 733)-net in base 8, because

1 times m-reduction [i] would yield (35, 135, 733)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85 831781 189301 088544 373989 689864 801456 767335 953870 455112 218685 001733 970688 989847 608163 275129 438882 059343 402666 742794 862676 > 8¹³⁵ [i]