Best Known (57, 57+57, s)-Nets in Base 3
(57, 57+57, 52)-Net over F3 — Constructive and digital
Digital (57, 114, 52)-net over F3, using
- 1 times m-reduction [i] based on digital (57, 115, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 42, 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, 73, 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, 42, 24)-net over F3, using
- (u, u+v)-construction [i] based on
(57, 57+57, 64)-Net over F3 — Digital
Digital (57, 114, 64)-net over F3, using
- t-expansion [i] based on digital (49, 114, 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
(57, 57+57, 449)-Net in Base 3 — Upper bound on s
There is no (57, 114, 450)-net in base 3, because
- 1 times m-reduction [i] would yield (57, 113, 450)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 870124 876026 760354 231187 065422 783172 944656 926071 933977 > 3113 [i]