Best Known (144−60, 144, s)-Nets in Base 5
(144−60, 144, 252)-Net over F5 — Constructive and digital
Digital (84, 144, 252)-net over F5, using
- 4 times m-reduction [i] based on digital (84, 148, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F25, using
(144−60, 144, 266)-Net over F5 — Digital
Digital (84, 144, 266)-net over F5, using
(144−60, 144, 6798)-Net in Base 5 — Upper bound on s
There is no (84, 144, 6799)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 45033 185839 798679 319315 093820 640125 184773 567090 714714 070933 757590 816781 591948 005493 892446 025704 124809 > 5144 [i]