Best Known (139, 252, s)-Nets in Base 4
(139, 252, 131)-Net over F4 — Constructive and digital
Digital (139, 252, 131)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 66, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (73, 186, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (10, 66, 27)-net over F4, using
(139, 252, 249)-Net over F4 — Digital
Digital (139, 252, 249)-net over F4, using
(139, 252, 3568)-Net in Base 4 — Upper bound on s
There is no (139, 252, 3569)-net in base 4, because
- 1 times m-reduction [i] would yield (139, 251, 3569)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 200829 833810 594369 934943 280234 481548 942384 001762 749328 036160 297105 679931 589226 215986 271804 532993 652441 380743 952446 669836 976939 947360 885042 272580 494952 > 4251 [i]