MinT - Best Known (142−74, 142, s)-Nets in Base 5

Best Known (142−74, 142, s)-Nets in Base 5

(142−74, 142, 82)-Net over F₅ — Constructive and digital

Digital (68, 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]

(142−74, 142, 132)-Net over F₅ — Digital

Digital (68, 142, 132)-net over F₅, using

t-expansion [i] based on digital (67, 142, 132)-net over F₅, using
- net from sequence [i] based on digital (67, 131)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(142−74, 142, 1736)-Net in Base 5 — Upper bound on s

There is no (68, 142, 1737)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1814 884879 923425 950903 456025 015041 032861 549395 327342 424409 902198 220136 011221 730822 741419 695050 186965 > 5¹⁴² [i]