MinT - Best Known (128−41, 128, s)-Nets in Base 5

Best Known (128−41, 128, s)-Nets in Base 5

(128−41, 128, 296)-Net over F₅ — Constructive and digital

Digital (87, 128, 296)-net over F₅, using

8 times m-reduction [i] based on digital (87, 136, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 68, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(128−41, 128, 700)-Net over F₅ — Digital

Digital (87, 128, 700)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−41, 128, 56963)-Net in Base 5 — Upper bound on s

There is no (87, 128, 56964)-net in base 5, because

1 times m-reduction [i] would yield (87, 127, 56964)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58788 887950 508844 787699 852071 022343 774053 848627 460677 963437 123676 267704 039406 362898 703105 > 5¹²⁷ [i]