MinT - Best Known (61−32, 61, s)-Nets in Base 8

Best Known (61−32, 61, s)-Nets in Base 8

(61−32, 61, 70)-Net over F₈ — Constructive and digital

Digital (29, 61, 70)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 20, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (9, 41, 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]

(61−32, 61, 99)-Net over F₈ — Digital

Digital (29, 61, 99)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(61−32, 61, 2684)-Net in Base 8 — Upper bound on s

There is no (29, 61, 2685)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 283099 115137 202222 162289 456421 196265 362628 237315 255441 > 8⁶¹ [i]