Best Known (178−57, 178, s)-Nets in Base 3
(178−57, 178, 162)-Net over F3 — Constructive and digital
Digital (121, 178, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 89, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(178−57, 178, 327)-Net over F3 — Digital
Digital (121, 178, 327)-net over F3, using
(178−57, 178, 5834)-Net in Base 3 — Upper bound on s
There is no (121, 178, 5835)-net in base 3, because
- 1 times m-reduction [i] would yield (121, 177, 5835)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2 824278 112544 223533 553846 715360 147162 402394 708562 533979 882629 114865 450048 530163 895209 > 3177 [i]