MinT - Best Known (26, 26+116, s)-Nets in Base 8

Best Known (26, 26+116, s)-Nets in Base 8

(26, 26+116, 65)-Net over F₈ — Constructive and digital

Digital (26, 142, 65)-net over F₈, using

t-expansion [i] based on digital (14, 142, 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]

(26, 26+116, 86)-Net over F₈ — Digital

Digital (26, 142, 86)-net over F₈, using

t-expansion [i] based on digital (25, 142, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(26, 26+116, 485)-Net in Base 8 — Upper bound on s

There is no (26, 142, 486)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186 422085 774304 235351 859479 968272 021449 330607 516686 350711 977161 150121 051750 502536 710172 341325 950269 408463 690127 268894 703145 008944 > 8¹⁴² [i]