MinT - Best Known (67, 133, s)-Nets in Base 5

Best Known (67, 133, s)-Nets in Base 5

(67, 133, 88)-Net over F₅ — Constructive and digital

Digital (67, 133, 88)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (3, 36, 16)-net over F₅, using
  - net from sequence [i] based on digital (3, 15)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 97, 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]

(67, 133, 135)-Net over F₅ — Digital

Digital (67, 133, 135)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 133, 2135)-Net in Base 5 — Upper bound on s

There is no (67, 133, 2136)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 927 436297 314413 774431 638045 151683 831496 606709 929527 724575 589275 011030 452242 149814 142846 339425 > 5¹³³ [i]