Best Known (39, 39+57, s)-Nets in Base 32
(39, 39+57, 162)-Net over F32 — Constructive and digital
Digital (39, 96, 162)-net over F32, using
- 1 times m-reduction [i] based on digital (39, 97, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 32, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 65, 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 (3, 32, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(39, 39+57, 288)-Net in Base 32 — Constructive
(39, 96, 288)-net in base 32, using
- 9 times m-reduction [i] based on (39, 105, 288)-net in base 32, using
- base change [i] based on digital (9, 75, 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, 75, 288)-net over F128, using
(39, 39+57, 291)-Net over F32 — Digital
Digital (39, 96, 291)-net over F32, using
- t-expansion [i] based on digital (38, 96, 291)-net over F32, using
- net from sequence [i] based on digital (38, 290)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 38 and N(F) ≥ 291, using
- net from sequence [i] based on digital (38, 290)-sequence over F32, using
(39, 39+57, 342)-Net in Base 32
(39, 96, 342)-net in base 32, using
- t-expansion [i] based on (38, 96, 342)-net in base 32, using
- 12 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- 12 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
(39, 39+57, 46587)-Net in Base 32 — Upper bound on s
There is no (39, 96, 46588)-net in base 32, because
- 1 times m-reduction [i] would yield (39, 95, 46588)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 97593 102290 089608 724596 321483 131992 016502 875708 955169 694975 888241 335657 215255 230011 028356 807544 324911 976135 641112 552416 658195 980382 095241 917560 > 3295 [i]