MinT - Best Known (124−58, 124, s)-Nets in Base 5

Best Known (124−58, 124, s)-Nets in Base 5

(124−58, 124, 132)-Net over F₅ — Constructive and digital

Digital (66, 124, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 62, 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]

(124−58, 124, 156)-Net over F₅ — Digital

Digital (66, 124, 156)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−58, 124, 2821)-Net in Base 5 — Upper bound on s

There is no (66, 124, 2822)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 471 613303 394208 169440 400271 248974 992379 877007 055881 779798 119111 851790 060426 708801 796505 > 5¹²⁴ [i]