MinT - Best Known (171−101, 171, s)-Nets in Base 8

Best Known (171−101, 171, s)-Nets in Base 8

(171−101, 171, 98)-Net over F₈ — Constructive and digital

Digital (70, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−101, 171, 144)-Net over F₈ — Digital

Digital (70, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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]

(171−101, 171, 156)-Net in Base 8

(70, 171, 156)-net in base 8, using

1 times m-reduction [i] based on (70, 172, 156)-net in base 8, using
- base change [i] based on digital (27, 129, 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]

(171−101, 171, 3242)-Net in Base 8 — Upper bound on s

There is no (70, 171, 3243)-net in base 8, because

1 times m-reduction [i] would yield (70, 170, 3243)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3383 847940 335385 976980 553039 977514 243045 784245 526136 153546 706223 879063 966074 042915 983181 213592 932295 193569 124156 619397 492542 244886 967697 080031 814382 986936 > 8¹⁷⁰ [i]