Best Known (21, 21+20, s)-Nets in Base 32
(21, 21+20, 162)-Net over F32 — Constructive and digital
Digital (21, 41, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (21, 43, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 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, 29, 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, 14, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(21, 21+20, 288)-Net in Base 32 — Constructive
(21, 41, 288)-net in base 32, using
- 1 times m-reduction [i] based on (21, 42, 288)-net in base 32, using
- base change [i] based on digital (9, 30, 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, 30, 288)-net over F128, using
(21, 21+20, 531)-Net over F32 — Digital
Digital (21, 41, 531)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3241, 531, F32, 20) (dual of [531, 490, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 1032, F32, 20) (dual of [1032, 991, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3239, 1024, F32, 20) (dual of [1024, 985, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3233, 1024, F32, 17) (dual of [1024, 991, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3241, 1032, F32, 20) (dual of [1032, 991, 21]-code), using
(21, 21+20, 216630)-Net in Base 32 — Upper bound on s
There is no (21, 41, 216631)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 51 422907 708160 202209 688259 533265 383243 939887 578060 961036 312338 > 3241 [i]