MinT - Best Known (81, 81+65, s)-Nets in Base 5

Best Known (81, 81+65, s)-Nets in Base 5

(81, 81+65, 132)-Net over F₅ — Constructive and digital

Digital (81, 146, 132)-net over F₅, using

t-expansion [i] based on digital (79, 146, 132)-net over F₅, using
- 4 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
  - trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
    - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
        a function field by GarcÃa and Quoos [i]

(81, 81+65, 212)-Net over F₅ — Digital

Digital (81, 146, 212)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+65, 4675)-Net in Base 5 — Upper bound on s

There is no (81, 146, 4676)-net in base 5, because

1 times m-reduction [i] would yield (81, 145, 4676)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224531 279852 911517 770169 837224 738239 988430 126474 081427 049137 961065 535909 355237 754592 767208 911484 289025 > 5¹⁴⁵ [i]