MinT - Best Known (71, 71+72, s)-Nets in Base 5

Best Known (71, 71+72, s)-Nets in Base 5

(71, 71+72, 90)-Net over F₅ — Constructive and digital

Digital (71, 143, 90)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (4, 40, 18)-net over F₅, using
  - net from sequence [i] based on digital (4, 17)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 103, 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]

(71, 71+72, 136)-Net over F₅ — Digital

Digital (71, 143, 136)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+72, 2107)-Net in Base 5 — Upper bound on s

There is no (71, 143, 2108)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9066 314123 373230 183075 137319 239822 274166 483473 837049 510769 204814 251866 556740 907018 972664 913671 741185 > 5¹⁴³ [i]