MinT - Best Known (60, 60+72, s)-Nets in Base 5

Best Known (60, 60+72, s)-Nets in Base 5

(60, 60+72, 82)-Net over F₅ — Constructive and digital

Digital (60, 132, 82)-net over F₅, using

t-expansion [i] based on digital (48, 132, 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]

(60, 60+72, 112)-Net over F₅ — Digital

Digital (60, 132, 112)-net over F₅, using

t-expansion [i] based on digital (57, 132, 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]

(60, 60+72, 1278)-Net in Base 5 — Upper bound on s

There is no (60, 132, 1279)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 185 914670 941798 570604 233750 554064 444716 304072 763012 396041 934417 904739 368629 749164 376630 304625 > 5¹³² [i]