MinT - Best Known (155−89, 155, s)-Nets in Base 8

Best Known (155−89, 155, s)-Nets in Base 8

(155−89, 155, 100)-Net over F₈ — Constructive and digital

Digital (66, 155, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 52, 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, 103, 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]

(155−89, 155, 144)-Net over F₈ — Digital

Digital (66, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(155−89, 155, 156)-Net in Base 8

(66, 155, 156)-net in base 8, using

1 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]

(155−89, 155, 3542)-Net in Base 8 — Upper bound on s

There is no (66, 155, 3543)-net in base 8, because

1 times m-reduction [i] would yield (66, 154, 3543)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 049525 923295 013489 174088 889938 255859 524719 619065 674332 766317 019928 517014 771610 742400 973962 446289 590698 692867 507038 001330 965289 315137 329580 > 8¹⁵⁴ [i]