Best Known (177, 177+59, s)-Nets in Base 3
(177, 177+59, 328)-Net over F3 — Constructive and digital
Digital (177, 236, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 59, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(177, 177+59, 974)-Net over F3 — Digital
Digital (177, 236, 974)-net over F3, using
(177, 177+59, 42867)-Net in Base 3 — Upper bound on s
There is no (177, 236, 42868)-net in base 3, because
- 1 times m-reduction [i] would yield (177, 235, 42868)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 13291 152348 814041 122649 512549 449010 813090 177100 209656 355015 455344 777623 179138 209215 087751 851198 957820 524739 562569 > 3235 [i]