MinT - Best Known (142−82, 142, s)-Nets in Base 5

Best Known (142−82, 142, s)-Nets in Base 5

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

Digital (60, 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]

(142−82, 142, 112)-Net over F₅ — Digital

Digital (60, 142, 112)-net over F₅, using

t-expansion [i] based on digital (57, 142, 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]

(142−82, 142, 1033)-Net in Base 5 — Upper bound on s

There is no (60, 142, 1034)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1835 530190 437580 253979 088303 703227 074687 740427 197416 146049 505632 915831 959839 247997 191944 426835 261225 > 5¹⁴² [i]