MinT - Best Known (35, 35+109, s)-Nets in Base 8

Best Known (35, 35+109, s)-Nets in Base 8

(35, 35+109, 65)-Net over F₈ — Constructive and digital

Digital (35, 144, 65)-net over F₈, using

t-expansion [i] based on digital (14, 144, 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]

(35, 35+109, 112)-Net over F₈ — Digital

Digital (35, 144, 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]

(35, 35+109, 704)-Net in Base 8 — Upper bound on s

There is no (35, 144, 705)-net in base 8, because

1 times m-reduction [i] would yield (35, 143, 705)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1481 192520 236620 766916 658375 159147 040197 959695 822520 005035 206735 324132 574180 150660 772141 286478 790846 608003 819963 983387 617284 284832 > 8¹⁴³ [i]