MinT - Best Known (124, 124+56, s)-Nets in Base 3

Best Known (124, 124+56, s)-Nets in Base 3

(124, 124+56, 192)-Net over F₃ — Constructive and digital

Digital (124, 180, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 60, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(124, 124+56, 361)-Net over F₃ — Digital

Digital (124, 180, 361)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+56, 6567)-Net in Base 3 — Upper bound on s

There is no (124, 180, 6568)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 479877 473726 418003 082197 153824 055247 460854 552699 940355 007222 642048 939581 083747 692097 > 3¹⁸⁰ [i]