MinT - Best Known (75, 75+73, s)-Nets in Base 5

Best Known (75, 75+73, s)-Nets in Base 5

(75, 75+73, 95)-Net over F₅ — Constructive and digital

Digital (75, 148, 95)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (8, 44, 23)-net over F₅, using
  - net from sequence [i] based on digital (8, 22)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 7, N(F)Â =Â 22, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using an explicitly constructive algebraic function field [i]
2. digital (31, 104, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(75, 75+73, 151)-Net over F₅ — Digital

Digital (75, 148, 151)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+73, 2525)-Net in Base 5 — Upper bound on s

There is no (75, 148, 2526)-net in base 5, because

1 times m-reduction [i] would yield (75, 147, 2526)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 672738 001051 454868 746038 301531 617715 063351 876407 488805 897023 213264 421648 249965 021752 222864 624568 450625 > 5¹⁴⁷ [i]