Best Known (84, 244, s)-Nets in Base 4
(84, 244, 104)-Net over F4 — Constructive and digital
Digital (84, 244, 104)-net over F4, using
- t-expansion [i] based on digital (73, 244, 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
(84, 244, 129)-Net over F4 — Digital
Digital (84, 244, 129)-net over F4, using
- t-expansion [i] based on digital (81, 244, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(84, 244, 635)-Net in Base 4 — Upper bound on s
There is no (84, 244, 636)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 826 997562 515676 769448 034710 138734 555763 222934 057849 367678 177149 809760 495573 037394 382356 253805 313189 119731 249943 531857 905700 583320 407784 383174 383255 > 4244 [i]