Best Known (216−67, 216, s)-Nets in Base 3
(216−67, 216, 204)-Net over F3 — Constructive and digital
Digital (149, 216, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 72, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
(216−67, 216, 427)-Net over F3 — Digital
Digital (149, 216, 427)-net over F3, using
(216−67, 216, 8417)-Net in Base 3 — Upper bound on s
There is no (149, 216, 8418)-net in base 3, because
- 1 times m-reduction [i] would yield (149, 215, 8418)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 822391 713553 286512 854253 880923 009380 104379 106984 154636 492019 284844 456204 939254 619338 824607 952627 825285 > 3215 [i]