MinT - Best Known (167−131, 167, s)-Nets in Base 8

Best Known (167−131, 167, s)-Nets in Base 8

(167−131, 167, 65)-Net over F₈ — Constructive and digital

Digital (36, 167, 65)-net over F₈, using

t-expansion [i] based on digital (14, 167, 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]

(167−131, 167, 112)-Net over F₈ — Digital

Digital (36, 167, 112)-net over F₈, using

t-expansion [i] based on digital (35, 167, 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]

(167−131, 167, 683)-Net in Base 8 — Upper bound on s

There is no (36, 167, 684)-net in base 8, because

1 times m-reduction [i] would yield (36, 166, 684)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 833823 212328 367646 845779 559563 887952 195576 709395 711552 049538 402151 983871 757441 914935 535828 821932 856191 281284 920214 284534 988692 685037 273913 468682 405362 > 8¹⁶⁶ [i]