MinT - Best Known (101−56, 101, s)-Nets in Base 5

Best Known (101−56, 101, s)-Nets in Base 5

(101−56, 101, 78)-Net over F₅ — Constructive and digital

Digital (45, 101, 78)-net over F₅, using

t-expansion [i] based on digital (38, 101, 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]

(101−56, 101, 88)-Net over F₅ — Digital

Digital (45, 101, 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]

(101−56, 101, 917)-Net in Base 5 — Upper bound on s

There is no (45, 101, 918)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 39777 642247 168306 321251 398363 431181 984582 367410 043667 304342 351213 750465 > 5¹⁰¹ [i]