Best Known (36, 69, s)-Nets in Base 32
(36, 69, 224)-Net over F32 — Constructive and digital
Digital (36, 69, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 25, 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 (11, 44, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (9, 25, 104)-net over F32, using
(36, 69, 288)-Net in Base 32 — Constructive
(36, 69, 288)-net in base 32, using
- t-expansion [i] based on (35, 69, 288)-net in base 32, using
- 22 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
- 22 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
(36, 69, 788)-Net over F32 — Digital
Digital (36, 69, 788)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3269, 788, F32, 33) (dual of [788, 719, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3269, 1042, F32, 33) (dual of [1042, 973, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3251, 1024, F32, 26) (dual of [1024, 973, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(326, 18, F32, 6) (dual of [18, 12, 7]-code or 18-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3269, 1042, F32, 33) (dual of [1042, 973, 34]-code), using
(36, 69, 547089)-Net in Base 32 — Upper bound on s
There is no (36, 69, 547090)-net in base 32, because
- 1 times m-reduction [i] would yield (36, 68, 547090)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 239802 610579 455632 957094 142230 567424 450619 863577 508129 846274 387297 570869 707697 065308 396598 308540 700353 > 3268 [i]