Best Known (128−67, 128, s)-Nets in Base 3
(128−67, 128, 52)-Net over F3 — Constructive and digital
Digital (61, 128, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 46, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (15, 82, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (13, 46, 24)-net over F3, using
(128−67, 128, 64)-Net over F3 — Digital
Digital (61, 128, 64)-net over F3, using
- t-expansion [i] based on digital (49, 128, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(128−67, 128, 419)-Net in Base 3 — Upper bound on s
There is no (61, 128, 420)-net in base 3, because
- 1 times m-reduction [i] would yield (61, 127, 420)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 989517 248402 388995 878912 491767 622141 021654 598526 713755 729225 > 3127 [i]