MinT - Best Known (66, 66+86, s)-Nets in Base 8

Best Known (66, 66+86, s)-Nets in Base 8

(66, 66+86, 110)-Net over F₈ — Constructive and digital

Digital (66, 152, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 52, 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, 100, 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]

(66, 66+86, 150)-Net over F₈ — Digital

Digital (66, 152, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+86, 156)-Net in Base 8

(66, 152, 156)-net in base 8, using

4 times m-reduction [i] based on (66, 156, 156)-net in base 8, using
- base change [i] based on digital (27, 117, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(66, 66+86, 3728)-Net in Base 8 — Upper bound on s

There is no (66, 152, 3729)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186931 826018 241065 847905 345718 219262 185470 466168 285616 317681 286904 762512 943249 794859 957365 842494 865093 506330 640528 109362 316300 828932 101440 > 8¹⁵² [i]