MinT - Best Known (52, 52+58, s)-Nets in Base 8

Best Known (52, 52+58, s)-Nets in Base 8

(52, 52+58, 110)-Net over F₈ — Constructive and digital

Digital (52, 110, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 38, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 72, 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]

(52, 52+58, 152)-Net over F₈ — Digital

Digital (52, 110, 152)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+58, 4423)-Net in Base 8 — Upper bound on s

There is no (52, 110, 4424)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2194 941328 412420 143819 902243 474374 755166 530318 314721 844360 267616 101124 067137 474780 085870 758160 405320 > 8¹¹⁰ [i]