MinT - Best Known (67, 142, s)-Nets in Base 5

Best Known (67, 142, s)-Nets in Base 5

(67, 142, 82)-Net over F₅ — Constructive and digital

Digital (67, 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]

(67, 142, 132)-Net over F₅ — Digital

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]

(67, 142, 1661)-Net in Base 5 — Upper bound on s

There is no (67, 142, 1662)-net in base 5, because

1 times m-reduction [i] would yield (67, 141, 1662)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 363 644416 738451 193458 810308 934114 865782 386439 976488 834352 404263 938923 643001 007702 747600 230752 203385 > 5¹⁴¹ [i]