Best Known (139−73, 139, s)-Nets in Base 3
(139−73, 139, 56)-Net over F3 — Constructive and digital
Digital (66, 139, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 51, 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 (15, 88, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 51, 28)-net over F3, using
(139−73, 139, 64)-Net over F3 — Digital
Digital (66, 139, 64)-net over F3, using
- t-expansion [i] based on digital (49, 139, 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
(139−73, 139, 447)-Net in Base 3 — Upper bound on s
There is no (66, 139, 448)-net in base 3, because
- 1 times m-reduction [i] would yield (66, 138, 448)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 742821 367550 517070 636381 662675 419811 766083 056989 307236 774017 151489 > 3138 [i]