MinT - Best Known (143−78, 143, s)-Nets in Base 5

Best Known (143−78, 143, s)-Nets in Base 5

(143−78, 143, 82)-Net over F₅ — Constructive and digital

Digital (65, 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]

(143−78, 143, 120)-Net over F₅ — Digital

Digital (65, 143, 120)-net over F₅, using

t-expansion [i] based on digital (61, 143, 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]

(143−78, 143, 1378)-Net in Base 5 — Upper bound on s

There is no (65, 143, 1379)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9135 978836 828404 085442 364872 843607 632632 793602 227693 612567 111319 379875 301318 786650 614628 733450 675125 > 5¹⁴³ [i]