Best Known (32, 32+35, s)-Nets in Base 16
(32, 32+35, 130)-Net over F16 — Constructive and digital
Digital (32, 67, 130)-net over F16, using
- 5 times m-reduction [i] based on digital (32, 72, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 26, 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
- digital (6, 46, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 26, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(32, 32+35, 177)-Net in Base 16 — Constructive
(32, 67, 177)-net in base 16, using
- 8 times m-reduction [i] based on (32, 75, 177)-net in base 16, using
- base change [i] based on digital (7, 50, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 50, 177)-net over F64, using
(32, 32+35, 211)-Net over F16 — Digital
Digital (32, 67, 211)-net over F16, using
(32, 32+35, 22620)-Net in Base 16 — Upper bound on s
There is no (32, 67, 22621)-net in base 16, because
- 1 times m-reduction [i] would yield (32, 66, 22621)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 29 659477 320081 346518 210759 506813 789127 142071 807006 473265 458774 359781 366323 496956 > 1666 [i]