MinT - Best Known (48, 48+28, s)-Nets in Base 5

Best Known (48, 48+28, s)-Nets in Base 5

(48, 48+28, 252)-Net over F₅ — Constructive and digital

Digital (48, 76, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 38, 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]

(48, 48+28, 259)-Net over F₅ — Digital

Digital (48, 76, 259)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+28, 9404)-Net in Base 5 — Upper bound on s

There is no (48, 76, 9405)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 132407 797299 492335 600420 514413 646882 231601 908851 713385 > 5⁷⁶ [i]