Best Known (131−69, 131, s)-Nets in Base 3
(131−69, 131, 52)-Net over F3 — Constructive and digital
Digital (62, 131, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 47, 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, 84, 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, 47, 24)-net over F3, using
(131−69, 131, 64)-Net over F3 — Digital
Digital (62, 131, 64)-net over F3, using
- t-expansion [i] based on digital (49, 131, 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
(131−69, 131, 419)-Net in Base 3 — Upper bound on s
There is no (62, 131, 420)-net in base 3, because
- 1 times m-reduction [i] would yield (62, 130, 420)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 113 773678 923932 036939 555999 108995 233412 017875 239443 849956 549625 > 3130 [i]