Best Known (17, 17+24, s)-Nets in Base 32
(17, 17+24, 120)-Net over F32 — Constructive and digital
Digital (17, 41, 120)-net over F32, using
- t-expansion [i] based on digital (11, 41, 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
(17, 17+24, 159)-Net over F32 — Digital
Digital (17, 41, 159)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3241, 159, F32, 2, 24) (dual of [(159, 2), 277, 25]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3239, 158, F32, 2, 24) (dual of [(158, 2), 277, 25]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,291P) [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3239, 158, F32, 2, 24) (dual of [(158, 2), 277, 25]-NRT-code), using
(17, 17+24, 258)-Net in Base 32 — Constructive
(17, 41, 258)-net in base 32, using
- 1 times m-reduction [i] based on (17, 42, 258)-net in base 32, using
- base change [i] based on (10, 35, 258)-net in base 64, using
- 1 times m-reduction [i] based on (10, 36, 258)-net in base 64, using
- base change [i] based on digital (1, 27, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 27, 258)-net over F256, using
- 1 times m-reduction [i] based on (10, 36, 258)-net in base 64, using
- base change [i] based on (10, 35, 258)-net in base 64, using
(17, 17+24, 289)-Net in Base 32
(17, 41, 289)-net in base 32, using
- 1 times m-reduction [i] based on (17, 42, 289)-net in base 32, using
- base change [i] based on (10, 35, 289)-net in base 64, using
- 1 times m-reduction [i] based on (10, 36, 289)-net in base 64, using
- base change [i] based on digital (1, 27, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 27, 289)-net over F256, using
- 1 times m-reduction [i] based on (10, 36, 289)-net in base 64, using
- base change [i] based on (10, 35, 289)-net in base 64, using
(17, 17+24, 23685)-Net in Base 32 — Upper bound on s
There is no (17, 41, 23686)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 51 427941 169944 462973 379174 227531 478747 276810 677028 695530 062672 > 3241 [i]