MinT - Best Known (64, 64+82, s)-Nets in Base 8

Best Known (64, 64+82, s)-Nets in Base 8

(64, 64+82, 110)-Net over F₈ — Constructive and digital

Digital (64, 146, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 50, 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, 96, 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]

(64, 64+82, 150)-Net over F₈ — Digital

Digital (64, 146, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+82, 156)-Net in Base 8

(64, 146, 156)-net in base 8, using

2 times m-reduction [i] based on (64, 148, 156)-net in base 8, using
- base change [i] based on digital (27, 111, 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]

(64, 64+82, 3764)-Net in Base 8 — Upper bound on s

There is no (64, 146, 3765)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 712152 459700 940099 738558 223959 730768 015104 590021 341592 355885 396883 772809 814516 838103 207797 186115 868970 884504 061127 729052 087394 476488 > 8¹⁴⁶ [i]