Best Known (36, 36+38, s)-Nets in Base 32
(36, 36+38, 202)-Net over F32 — Constructive and digital
Digital (36, 74, 202)-net over F32, using
- 2 times m-reduction [i] based on digital (36, 76, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 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 (9, 49, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 27, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(36, 36+38, 288)-Net in Base 32 — Constructive
(36, 74, 288)-net in base 32, using
- t-expansion [i] based on (35, 74, 288)-net in base 32, using
- 17 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
- base change [i] based on digital (9, 65, 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, 65, 288)-net over F128, using
- 17 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
(36, 36+38, 516)-Net over F32 — Digital
Digital (36, 74, 516)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3274, 516, F32, 2, 38) (dual of [(516, 2), 958, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3274, 1032, F32, 38) (dual of [1032, 958, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(34) [i] based on
- linear OA(3272, 1024, F32, 38) (dual of [1024, 952, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3266, 1024, F32, 35) (dual of [1024, 958, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(37) ⊂ Ce(34) [i] based on
- OOA 2-folding [i] based on linear OA(3274, 1032, F32, 38) (dual of [1032, 958, 39]-code), using
(36, 36+38, 186206)-Net in Base 32 — Upper bound on s
There is no (36, 74, 186207)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2405 069293 973308 675467 545695 159674 128289 984595 570520 296144 962135 048965 102835 970529 743429 538776 510064 591222 465420 > 3274 [i]