Best Known (128, 128+78, s)-Nets in Base 4
(128, 128+78, 137)-Net over F4 — Constructive and digital
Digital (128, 206, 137)-net over F4, using
- 2 times m-reduction [i] based on digital (128, 208, 137)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 55, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (73, 153, 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 (15, 55, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(128, 128+78, 361)-Net over F4 — Digital
Digital (128, 206, 361)-net over F4, using
(128, 128+78, 7737)-Net in Base 4 — Upper bound on s
There is no (128, 206, 7738)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10579 220548 516940 286234 942040 606869 871601 474243 703216 072946 620014 032171 171271 898827 943018 549727 662819 895270 522536 195596 759308 > 4206 [i]