MinT - Best Known (141−95, 141, s)-Nets in Base 5

Best Known (141−95, 141, s)-Nets in Base 5

(141−95, 141, 78)-Net over F₅ — Constructive and digital

Digital (46, 141, 78)-net over F₅, using

t-expansion [i] based on digital (38, 141, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(141−95, 141, 88)-Net over F₅ — Digital

Digital (46, 141, 88)-net over F₅, using

t-expansion [i] based on digital (45, 141, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(141−95, 141, 520)-Net in Base 5 — Upper bound on s

There is no (46, 141, 521)-net in base 5, because

1 times m-reduction [i] would yield (46, 140, 521)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 73 431304 533713 536710 160521 064762 713094 615651 052183 626129 400229 762949 491341 267064 575889 979176 766125 > 5¹⁴⁰ [i]