Best Known (162−51, 162, s)-Nets in Base 4
(162−51, 162, 312)-Net over F4 — Constructive and digital
Digital (111, 162, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 54, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
(162−51, 162, 572)-Net over F4 — Digital
Digital (111, 162, 572)-net over F4, using
(162−51, 162, 25552)-Net in Base 4 — Upper bound on s
There is no (111, 162, 25553)-net in base 4, because
- 1 times m-reduction [i] would yield (111, 161, 25553)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 8 551977 136918 037209 182044 144318 577849 704421 631684 935087 523905 404870 558931 521056 487891 024086 105120 > 4161 [i]