MinT - Best Known (143−85, 143, s)-Nets in Base 5

Best Known (143−85, 143, s)-Nets in Base 5

(143−85, 143, 82)-Net over F₅ — Constructive and digital

Digital (58, 143, 82)-net over F₅, using

t-expansion [i] based on digital (48, 143, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(143−85, 143, 112)-Net over F₅ — Digital

Digital (58, 143, 112)-net over F₅, using

t-expansion [i] based on digital (57, 143, 112)-net over F₅, using
- net from sequence [i] based on digital (57, 111)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 57 and N(F) ≥ 112, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(143−85, 143, 921)-Net in Base 5 — Upper bound on s

There is no (58, 143, 922)-net in base 5, because

1 times m-reduction [i] would yield (58, 142, 922)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1794 611531 230995 050454 848823 193480 536727 046774 680070 935316 247929 917758 605872 664216 599193 585244 839745 > 5¹⁴² [i]