Best Known (23, 47, s)-Nets in Base 32
(23, 47, 162)-Net over F32 — Constructive and digital
Digital (23, 47, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (23, 49, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 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, 33, 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, 16, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(23, 47, 288)-Net in Base 32 — Constructive
(23, 47, 288)-net in base 32, using
- 2 times m-reduction [i] based on (23, 49, 288)-net in base 32, using
- base change [i] based on digital (9, 35, 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, 35, 288)-net over F128, using
(23, 47, 460)-Net over F32 — Digital
Digital (23, 47, 460)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3247, 460, F32, 2, 24) (dual of [(460, 2), 873, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 513, F32, 2, 24) (dual of [(513, 2), 979, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3247, 1026, F32, 24) (dual of [1026, 979, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(3247, 1024, F32, 24) (dual of [1024, 977, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3245, 1024, F32, 23) (dual of [1024, 979, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(3247, 1026, F32, 24) (dual of [1026, 979, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 513, F32, 2, 24) (dual of [(513, 2), 979, 25]-NRT-code), using
(23, 47, 134014)-Net in Base 32 — Upper bound on s
There is no (23, 47, 134015)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 55217 052287 631660 842194 488532 088794 091007 903035 728432 812905 906719 433373 > 3247 [i]