MinT - Best Known (36, 154, s)-Nets in Base 8

Best Known (36, 154, s)-Nets in Base 8

(36, 154, 65)-Net over F₈ — Constructive and digital

Digital (36, 154, 65)-net over F₈, using

t-expansion [i] based on digital (14, 154, 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]

(36, 154, 112)-Net over F₈ — Digital

Digital (36, 154, 112)-net over F₈, using

t-expansion [i] based on digital (35, 154, 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]

(36, 154, 705)-Net in Base 8 — Upper bound on s

There is no (36, 154, 706)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 664519 202511 924506 903421 384696 920007 329214 727228 127752 873314 644828 836145 315786 088626 707982 296702 781617 890402 754478 454348 442651 306187 078880 > 8¹⁵⁴ [i]