MinT - Best Known (121−66, 121, s)-Nets in Base 8

Best Known (121−66, 121, s)-Nets in Base 8

(121−66, 121, 100)-Net over F₈ — Constructive and digital

Digital (55, 121, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 41, 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, 80, 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]

(121−66, 121, 144)-Net over F₈ — Digital

Digital (55, 121, 144)-net over F₈, using

t-expansion [i] based on digital (45, 121, 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]

(121−66, 121, 3830)-Net in Base 8 — Upper bound on s

There is no (55, 121, 3831)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 880216 592050 286322 744240 886193 496913 256663 456762 096805 495512 714275 869994 584013 292623 160206 840357 727288 702890 > 8¹²¹ [i]