MinT - Best Known (150−89, 150, s)-Nets in Base 8

Best Known (150−89, 150, s)-Nets in Base 8

(150−89, 150, 98)-Net over F₈ — Constructive and digital

Digital (61, 150, 98)-net over F₈, using

t-expansion [i] based on digital (37, 150, 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]

(150−89, 150, 144)-Net over F₈ — Digital

Digital (61, 150, 144)-net over F₈, using

t-expansion [i] based on digital (45, 150, 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]

(150−89, 150, 2790)-Net in Base 8 — Upper bound on s

There is no (61, 150, 2791)-net in base 8, because

1 times m-reduction [i] would yield (61, 149, 2791)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 364 654946 698267 724671 181069 039236 037091 411846 140156 048992 580720 887021 977257 103379 075080 272827 162436 903177 443779 448825 442028 447670 670520 > 8¹⁴⁹ [i]