MinT - Best Known (140−90, 140, s)-Nets in Base 8

Best Known (140−90, 140, s)-Nets in Base 8

(140−90, 140, 98)-Net over F₈ — Constructive and digital

Digital (50, 140, 98)-net over F₈, using

t-expansion [i] based on digital (37, 140, 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]

(140−90, 140, 144)-Net over F₈ — Digital

Digital (50, 140, 144)-net over F₈, using

t-expansion [i] based on digital (45, 140, 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]

(140−90, 140, 1596)-Net in Base 8 — Upper bound on s

There is no (50, 140, 1597)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 775547 268409 933848 444152 473518 895885 986126 172933 112419 965548 950435 404919 384027 707284 544180 604767 649876 261227 629767 367379 823544 > 8¹⁴⁰ [i]