MinT - Best Known (101−67, 101, s)-Nets in Base 8

Best Known (101−67, 101, s)-Nets in Base 8

(101−67, 101, 65)-Net over F₈ — Constructive and digital

Digital (34, 101, 65)-net over F₈, using

t-expansion [i] based on digital (14, 101, 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]

(101−67, 101, 98)-Net over F₈ — Digital

Digital (34, 101, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(101−67, 101, 1004)-Net in Base 8 — Upper bound on s

There is no (34, 101, 1005)-net in base 8, because

1 times m-reduction [i] would yield (34, 100, 1005)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 049480 386064 467399 132562 588196 381553 418426 559171 032748 431137 438299 642162 971087 863504 315364 > 8¹⁰⁰ [i]