MinT - Best Known (124, 124+50, s)-Nets in Base 3

Best Known (124, 124+50, s)-Nets in Base 3

(124, 124+50, 252)-Net over F₃ — Constructive and digital

Digital (124, 174, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 58, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(124, 124+50, 454)-Net over F₃ — Digital

Digital (124, 174, 454)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+50, 10625)-Net in Base 3 — Upper bound on s

There is no (124, 174, 10626)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104551 468369 135732 061757 712035 419831 657019 827879 907442 772833 660494 223075 248887 974293 > 3¹⁷⁴ [i]