Best Known (195−71, 195, s)-Nets in Base 3
(195−71, 195, 156)-Net over F3 — Constructive and digital
Digital (124, 195, 156)-net over F3, using
- 9 times m-reduction [i] based on digital (124, 204, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 102, 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
- trace code for nets [i] based on digital (22, 102, 78)-net over F9, using
(195−71, 195, 239)-Net over F3 — Digital
Digital (124, 195, 239)-net over F3, using
(195−71, 195, 3033)-Net in Base 3 — Upper bound on s
There is no (124, 195, 3034)-net in base 3, because
- 1 times m-reduction [i] would yield (124, 194, 3034)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 365 960298 357828 053574 374563 007943 049127 548102 321173 784369 913274 141982 003042 487299 250757 983025 > 3194 [i]