MinT - Best Known (66−23, 66, s)-Nets in Base 5

Best Known (66−23, 66, s)-Nets in Base 5

(66−23, 66, 252)-Net over F₅ — Constructive and digital

Digital (43, 66, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 33, 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]

(66−23, 66, 294)-Net over F₅ — Digital

Digital (43, 66, 294)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−23, 66, 16558)-Net in Base 5 — Upper bound on s

There is no (43, 66, 16559)-net in base 5, because

1 times m-reduction [i] would yield (43, 65, 16559)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2710 905039 571958 854588 990090 271685 728400 532885 > 5⁶⁵ [i]