Best Known (69−37, 69, s)-Nets in Base 32
(69−37, 69, 196)-Net over F32 — Constructive and digital
Digital (32, 69, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 44, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 25, 98)-net over F32, using
(69−37, 69, 288)-Net in Base 32 — Constructive
(32, 69, 288)-net in base 32, using
- t-expansion [i] based on (31, 69, 288)-net in base 32, using
- 8 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- 8 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
(69−37, 69, 362)-Net over F32 — Digital
Digital (32, 69, 362)-net over F32, using
(69−37, 69, 118265)-Net in Base 32 — Upper bound on s
There is no (32, 69, 118266)-net in base 32, because
- 1 times m-reduction [i] would yield (32, 68, 118266)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 239999 954647 139948 596602 330213 612380 310652 129605 644058 409917 669757 579724 882255 517758 340147 316118 625284 > 3268 [i]