MinT - Best Known (128−53, 128, s)-Nets in Base 5

Best Known (128−53, 128, s)-Nets in Base 5

(128−53, 128, 252)-Net over F₅ — Constructive and digital

Digital (75, 128, 252)-net over F₅, using

2 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 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]

(128−53, 128, 6826)-Net in Base 5 — Upper bound on s

There is no (75, 128, 6827)-net in base 5, because

1 times m-reduction [i] would yield (75, 127, 6827)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58785 309642 411367 387630 126461 811581 766848 289467 664386 496896 701652 729934 848130 535529 063193 > 5¹²⁷ [i]