Best Known (19−11, 19, s)-Nets in Base 32
(19−11, 19, 99)-Net over F32 — Constructive and digital
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
(19−11, 19, 113)-Net over F32 — Digital
Digital (8, 19, 113)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3219, 113, F32, 11) (dual of [113, 94, 12]-code), using
- 27 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 20 times 0) [i] based on linear OA(3216, 83, F32, 11) (dual of [83, 67, 12]-code), using
- extended algebraic-geometric code AGe(F,71P) [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 83, using
- 27 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 20 times 0) [i] based on linear OA(3216, 83, F32, 11) (dual of [83, 67, 12]-code), using
(19−11, 19, 257)-Net in Base 32 — Constructive
(8, 19, 257)-net in base 32, using
- 2 times m-reduction [i] based on (8, 21, 257)-net in base 32, using
- base change [i] based on (2, 15, 257)-net in base 128, using
- 1 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- 1 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on (2, 15, 257)-net in base 128, using
(19−11, 19, 22027)-Net in Base 32 — Upper bound on s
There is no (8, 19, 22028)-net in base 32, because
- 1 times m-reduction [i] would yield (8, 18, 22028)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1237 985622 731679 348927 463602 > 3218 [i]