MinT - Best Known (62, 159, s)-Nets in Base 8

Best Known (62, 159, s)-Nets in Base 8

(62, 159, 98)-Net over F₈ — Constructive and digital

Digital (62, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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, 159, 144)-Net over F₈ — Digital

Digital (62, 159, 144)-net over F₈, using

t-expansion [i] based on digital (45, 159, 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, 159, 2483)-Net in Base 8 — Upper bound on s

There is no (62, 159, 2484)-net in base 8, because

1 times m-reduction [i] would yield (62, 158, 2484)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49019 903867 656223 050308 407561 919381 786408 919319 454245 518951 956989 470790 859892 006445 650968 011787 258233 815565 246329 049042 898331 365651 155795 631765 > 8¹⁵⁸ [i]