MinT - Best Known (81, 81+47, s)-Nets in Base 5

Best Known (81, 81+47, s)-Nets in Base 5

(81, 81+47, 252)-Net over F₅ — Constructive and digital

Digital (81, 128, 252)-net over F₅, using

14 times m-reduction [i] based on digital (81, 142, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 71, 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]

(81, 81+47, 388)-Net over F₅ — Digital

Digital (81, 128, 388)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+47, 17041)-Net in Base 5 — Upper bound on s

There is no (81, 128, 17042)-net in base 5, because

1 times m-reduction [i] would yield (81, 127, 17042)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58839 315199 852400 585461 766026 145484 207128 306089 379546 414993 930930 600096 548470 085114 130025 > 5¹²⁷ [i]