Best Known (82−69, 82, s)-Nets in Base 32
(82−69, 82, 120)-Net over F32 — Constructive and digital
Digital (13, 82, 120)-net over F32, using
- t-expansion [i] based on digital (11, 82, 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
(82−69, 82, 129)-Net over F32 — Digital
Digital (13, 82, 129)-net over F32, using
- t-expansion [i] based on digital (12, 82, 129)-net over F32, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 12 and N(F) ≥ 129, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
(82−69, 82, 1664)-Net in Base 32 — Upper bound on s
There is no (13, 82, 1665)-net in base 32, because
- 1 times m-reduction [i] would yield (13, 81, 1665)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 83 005517 582538 299388 154207 063315 158986 005561 461314 813316 723087 888349 843728 716414 638242 286436 196974 829570 997535 900458 156992 > 3281 [i]