MinT - Best Known (62, 62+87, s)-Nets in Base 8

Best Known (62, 62+87, s)-Nets in Base 8

(62, 62+87, 98)-Net over F₈ — Constructive and digital

Digital (62, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(62, 62+87, 144)-Net over F₈ — Digital

Digital (62, 149, 144)-net over F₈, using

t-expansion [i] based on digital (45, 149, 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]

(62, 62+87, 3068)-Net in Base 8 — Upper bound on s

There is no (62, 149, 3069)-net in base 8, because

1 times m-reduction [i] would yield (62, 148, 3069)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 018881 096097 877456 651582 230230 708362 769863 677572 052698 903669 015799 784739 873292 249596 155474 871508 443473 063852 695528 879143 205772 258940 > 8¹⁴⁸ [i]