MinT - Best Known (63, 63+53, s)-Nets in Base 5

Best Known (63, 63+53, s)-Nets in Base 5

(63, 63+53, 132)-Net over F₅ — Constructive and digital

Digital (63, 116, 132)-net over F₅, using

2 times m-reduction [i] based on digital (63, 118, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 59, 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]

(63, 63+53, 160)-Net over F₅ — Digital

Digital (63, 116, 160)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+53, 3238)-Net in Base 5 — Upper bound on s

There is no (63, 116, 3239)-net in base 5, because

1 times m-reduction [i] would yield (63, 115, 3239)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 242 399243 551211 643197 536431 250859 349905 006158 569809 701771 536164 363647 371547 146137 > 5¹¹⁵ [i]