MinT - Best Known (55, 55+62, s)-Nets in Base 8

Best Known (55, 55+62, s)-Nets in Base 8

(55, 55+62, 111)-Net over F₈ — Constructive and digital

Digital (55, 117, 111)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (10, 41, 46)-net over F₈, using
  - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
2. digital (14, 76, 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]

(55, 55+62, 156)-Net over F₈ — Digital

Digital (55, 117, 156)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+62, 4523)-Net in Base 8 — Upper bound on s

There is no (55, 117, 4524)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4590 255422 613704 594582 421197 556777 346988 434227 642510 232398 901437 503704 842074 498641 484769 560927 581656 691752 > 8¹¹⁷ [i]