Best Known (8, 18, s)-Nets in Base 32
(8, 18, 99)-Net over F32 — Constructive and digital
Digital (8, 18, 99)-net over F32, using
- 1 times m-reduction [i] based on digital (8, 19, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 11, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(8, 18, 142)-Net over F32 — Digital
Digital (8, 18, 142)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3218, 142, F32, 10) (dual of [142, 124, 11]-code), using
- 101 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 8 times 0, 1, 16 times 0, 1, 28 times 0, 1, 42 times 0) [i] based on linear OA(3210, 33, F32, 10) (dual of [33, 23, 11]-code or 33-arc in PG(9,32)), using
- extended Reed–Solomon code RSe(23,32) [i]
- 101 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 8 times 0, 1, 16 times 0, 1, 28 times 0, 1, 42 times 0) [i] based on linear OA(3210, 33, F32, 10) (dual of [33, 23, 11]-code or 33-arc in PG(9,32)), using
(8, 18, 258)-Net in Base 32 — Constructive
(8, 18, 258)-net in base 32, using
- base change [i] based on (5, 15, 258)-net in base 64, using
- 1 times m-reduction [i] based on (5, 16, 258)-net in base 64, using
- base change [i] based on digital (1, 12, 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, 12, 258)-net over F256, using
- 1 times m-reduction [i] based on (5, 16, 258)-net in base 64, using
(8, 18, 289)-Net in Base 32
(8, 18, 289)-net in base 32, using
- base change [i] based on (5, 15, 289)-net in base 64, using
- 1 times m-reduction [i] based on (5, 16, 289)-net in base 64, using
- base change [i] based on digital (1, 12, 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, 12, 289)-net over F256, using
- 1 times m-reduction [i] based on (5, 16, 289)-net in base 64, using
(8, 18, 22027)-Net in Base 32 — Upper bound on s
There is no (8, 18, 22028)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1237 985622 731679 348927 463602 > 3218 [i]