Best Known (99, 99+59, s)-Nets in Base 3
(99, 99+59, 148)-Net over F3 — Constructive and digital
Digital (99, 158, 148)-net over F3, using
- 6 times m-reduction [i] based on digital (99, 164, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 82, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 82, 74)-net over F9, using
(99, 99+59, 186)-Net over F3 — Digital
Digital (99, 158, 186)-net over F3, using
(99, 99+59, 2205)-Net in Base 3 — Upper bound on s
There is no (99, 158, 2206)-net in base 3, because
- 1 times m-reduction [i] would yield (99, 157, 2206)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 810 421812 215212 856694 356215 107353 808175 278384 018121 778406 836953 649885 284389 > 3157 [i]