MinT - Best Known (66, 66+39, s)-Nets in Base 5

Best Known (66, 66+39, s)-Nets in Base 5

(66, 66+39, 252)-Net over F₅ — Constructive and digital

Digital (66, 105, 252)-net over F₅, using

7 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(66, 66+39, 316)-Net over F₅ — Digital

Digital (66, 105, 316)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+39, 13263)-Net in Base 5 — Upper bound on s

There is no (66, 105, 13264)-net in base 5, because

1 times m-reduction [i] would yield (66, 104, 13264)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 936365 071648 301964 486284 173613 915723 530502 964538 551382 892744 878378 722625 > 5¹⁰⁴ [i]