MinT - Best Known (52, 52+71, s)-Nets in Base 8

Best Known (52, 52+71, s)-Nets in Base 8

(52, 52+71, 98)-Net over F₈ — Constructive and digital

Digital (52, 123, 98)-net over F₈, using

t-expansion [i] based on digital (37, 123, 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]

(52, 52+71, 144)-Net over F₈ — Digital

Digital (52, 123, 144)-net over F₈, using

t-expansion [i] based on digital (45, 123, 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]

(52, 52+71, 2771)-Net in Base 8 — Upper bound on s

There is no (52, 123, 2772)-net in base 8, because

1 times m-reduction [i] would yield (52, 122, 2772)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 151 997099 519870 676045 312242 369739 968726 364430 189820 602922 491040 354301 677527 282370 222133 043715 692310 838639 344378 > 8¹²² [i]