Best Known (29, 29+26, s)-Nets in Base 32
(29, 29+26, 202)-Net over F32 — Constructive and digital
Digital (29, 55, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 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, 35, 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, 20, 98)-net over F32, using
(29, 29+26, 290)-Net in Base 32 — Constructive
(29, 55, 290)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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
- (16, 42, 257)-net in base 32, using
- base change [i] based on (9, 35, 257)-net in base 64, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on (9, 35, 257)-net in base 64, using
- digital (0, 13, 33)-net over F32, using
(29, 29+26, 759)-Net over F32 — Digital
Digital (29, 55, 759)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3255, 759, F32, 26) (dual of [759, 704, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3255, 1038, F32, 26) (dual of [1038, 983, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- 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(3241, 1024, F32, 21) (dual of [1024, 983, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(324, 14, F32, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3255, 1038, F32, 26) (dual of [1038, 983, 27]-code), using
(29, 29+26, 426560)-Net in Base 32 — Upper bound on s
There is no (29, 55, 426561)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 60710 185985 981152 595235 690162 394443 954627 711221 013124 175440 667859 502378 240819 679424 > 3255 [i]