Best Known (125, 125+81, s)-Nets in Base 3
(125, 125+81, 156)-Net over F3 — Constructive and digital
Digital (125, 206, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 103, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(125, 125+81, 201)-Net over F3 — Digital
Digital (125, 206, 201)-net over F3, using
(125, 125+81, 2158)-Net in Base 3 — Upper bound on s
There is no (125, 206, 2159)-net in base 3, because
- 1 times m-reduction [i] would yield (125, 205, 2159)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 64 907501 348838 614848 221298 520195 867460 452919 939189 403153 022216 784392 871942 071155 372722 251253 503665 > 3205 [i]