MinT - Best Known (142−80, 142, s)-Nets in Base 5

Best Known (142−80, 142, s)-Nets in Base 5

(142−80, 142, 82)-Net over F₅ — Constructive and digital

Digital (62, 142, 82)-net over F₅, using

t-expansion [i] based on digital (48, 142, 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]

(142−80, 142, 120)-Net over F₅ — Digital

Digital (62, 142, 120)-net over F₅, using

t-expansion [i] based on digital (61, 142, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(142−80, 142, 1164)-Net in Base 5 — Upper bound on s

There is no (62, 142, 1165)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1796 663982 856848 999909 203639 248550 263573 627767 770492 739662 531775 166874 731016 497455 465270 226388 438625 > 5¹⁴² [i]