Best Known (59, 59+46, s)-Nets in Base 4
(59, 59+46, 130)-Net over F4 — Constructive and digital
Digital (59, 105, 130)-net over F4, using
- 1 times m-reduction [i] based on digital (59, 106, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 53, 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, 53, 65)-net over F16, using
(59, 59+46, 1742)-Net in Base 4 — Upper bound on s
There is no (59, 105, 1743)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1648 579915 996316 778045 348185 398366 818012 137163 294218 473151 458000 > 4105 [i]