Best Known (68, 68+51, s)-Nets in Base 4
(68, 68+51, 130)-Net over F4 — Constructive and digital
Digital (68, 119, 130)-net over F4, using
- 5 times m-reduction [i] based on digital (68, 124, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 62, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 62, 65)-net over F16, using
(68, 68+51, 150)-Net over F4 — Digital
Digital (68, 119, 150)-net over F4, using
(68, 68+51, 2336)-Net in Base 4 — Upper bound on s
There is no (68, 119, 2337)-net in base 4, because
- 1 times m-reduction [i] would yield (68, 118, 2337)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 111583 685562 389747 178667 527499 632243 279009 468366 139111 606165 620178 839568 > 4118 [i]