Best Known (44, 78, s)-Nets in Base 32
(44, 78, 240)-Net over F32 — Constructive and digital
Digital (44, 78, 240)-net over F32, using
- 10 times m-reduction [i] based on digital (44, 88, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 33, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 55, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 33, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(44, 78, 513)-Net in Base 32 — Constructive
(44, 78, 513)-net in base 32, using
- 18 times m-reduction [i] based on (44, 96, 513)-net in base 32, using
- base change [i] based on digital (28, 80, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 80, 513)-net over F64, using
(44, 78, 1550)-Net over F32 — Digital
Digital (44, 78, 1550)-net over F32, using
(44, 78, 1864505)-Net in Base 32 — Upper bound on s
There is no (44, 78, 1864506)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2521 729383 970096 522042 453825 012318 506071 122969 348803 050444 518111 203397 729900 013203 355284 915084 377283 106620 487116 543135 > 3278 [i]