MinT - Best Known (47, 47+126, s)-Nets in Base 8

Best Known (47, 47+126, s)-Nets in Base 8

(47, 47+126, 98)-Net over F₈ — Constructive and digital

Digital (47, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(47, 47+126, 144)-Net over F₈ — Digital

Digital (47, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(47, 47+126, 1008)-Net in Base 8 — Upper bound on s

There is no (47, 173, 1009)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 741565 327128 578205 983841 983100 221977 650354 244121 699858 070169 178082 046603 759015 946366 429182 284302 164933 587073 839834 045150 814317 491981 903120 214078 754887 431360 > 8¹⁷³ [i]