MinT - Best Known (173−123, 173, s)-Nets in Base 8

Best Known (173−123, 173, s)-Nets in Base 8

(173−123, 173, 98)-Net over F₈ — Constructive and digital

Digital (50, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(173−123, 173, 144)-Net over F₈ — Digital

Digital (50, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(173−123, 173, 1146)-Net in Base 8 — Upper bound on s

There is no (50, 173, 1147)-net in base 8, because

1 times m-reduction [i] would yield (50, 172, 1147)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 223779 871692 636069 706989 899081 845370 259912 977296 285892 068288 304473 252230 926826 309958 051705 306392 909834 314958 702237 405953 103262 817819 692045 593419 096776 932640 > 8¹⁷² [i]