MinT - Best Known (121−53, 121, s)-Nets in Base 5

Best Known (121−53, 121, s)-Nets in Base 5

(121−53, 121, 132)-Net over F₅ — Constructive and digital

Digital (68, 121, 132)-net over F₅, using

7 times m-reduction [i] based on digital (68, 128, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 64, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(121−53, 121, 192)-Net over F₅ — Digital

Digital (68, 121, 192)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−53, 121, 4419)-Net in Base 5 — Upper bound on s

There is no (68, 121, 4420)-net in base 5, because

1 times m-reduction [i] would yield (68, 120, 4420)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 753842 047742 941882 747755 634196 879212 101845 371099 011310 062736 737489 485618 471643 818689 > 5¹²⁰ [i]