MinT - Best Known (152−87, 152, s)-Nets in Base 8

Best Known (152−87, 152, s)-Nets in Base 8

(152−87, 152, 100)-Net over F₈ — Constructive and digital

Digital (65, 152, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 51, 35)-net over F₈, using
  - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [i]
2. digital (14, 101, 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]

(152−87, 152, 144)-Net over F₈ — Digital

Digital (65, 152, 144)-net over F₈, using

t-expansion [i] based on digital (45, 152, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(152−87, 152, 156)-Net in Base 8

(65, 152, 156)-net in base 8, using

base change [i] based on digital (27, 114, 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]

(152−87, 152, 3551)-Net in Base 8 — Upper bound on s

There is no (65, 152, 3552)-net in base 8, because

1 times m-reduction [i] would yield (65, 151, 3552)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23455 318892 534939 894773 035523 664479 371236 050119 113806 869843 974916 326621 028242 021841 004833 676977 460028 495824 992230 233657 019357 049091 189374 > 8¹⁵¹ [i]