MinT - Best Known (162−101, 162, s)-Nets in Base 8

Best Known (162−101, 162, s)-Nets in Base 8

(162−101, 162, 98)-Net over F₈ — Constructive and digital

Digital (61, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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]

(162−101, 162, 144)-Net over F₈ — Digital

Digital (61, 162, 144)-net over F₈, using

t-expansion [i] based on digital (45, 162, 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]

(162−101, 162, 2220)-Net in Base 8 — Upper bound on s

There is no (61, 162, 2221)-net in base 8, because

1 times m-reduction [i] would yield (61, 161, 2221)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 418529 371763 939807 613174 702223 433379 418783 818261 944778 353708 770118 723377 641447 321998 805597 148158 660589 934369 967995 476572 214727 770591 964003 798192 > 8¹⁶¹ [i]