MinT - Best Known (135−90, 135, s)-Nets in Base 8

Best Known (135−90, 135, s)-Nets in Base 8

(135−90, 135, 98)-Net over F₈ — Constructive and digital

Digital (45, 135, 98)-net over F₈, using

t-expansion [i] based on digital (37, 135, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(135−90, 135, 144)-Net over F₈ — Digital

Digital (45, 135, 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]

(135−90, 135, 1261)-Net in Base 8 — Upper bound on s

There is no (45, 135, 1262)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85 460971 931498 822322 662400 870675 271263 746192 193053 817984 764142 672531 180371 371853 419127 993330 781204 716013 027454 193186 362797 > 8¹³⁵ [i]