Best Known (39, 39+34, s)-Nets in Base 32
(39, 39+34, 240)-Net over F32 — Constructive and digital
Digital (39, 73, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 28, 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 (11, 45, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 28, 120)-net over F32, using
(39, 39+34, 301)-Net in Base 32 — Constructive
(39, 73, 301)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- (21, 55, 257)-net in base 32, using
- 1 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- base change [i] based on digital (0, 35, 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, 35, 257)-net over F256, using
- 1 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- digital (1, 18, 44)-net over F32, using
(39, 39+34, 990)-Net over F32 — Digital
Digital (39, 73, 990)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3273, 990, F32, 34) (dual of [990, 917, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 1050, F32, 34) (dual of [1050, 977, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(23) [i] based on
- linear OA(3264, 1024, F32, 34) (dual of [1024, 960, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 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(329, 26, F32, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,32)), using
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- Reed–Solomon code RS(23,32) [i]
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- construction X applied to Ce(33) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(3273, 1050, F32, 34) (dual of [1050, 977, 35]-code), using
(39, 39+34, 672773)-Net in Base 32 — Upper bound on s
There is no (39, 73, 672774)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 75 153719 326126 766494 644142 908162 083930 119283 162096 471899 342800 262749 001524 072611 912721 265912 996560 678216 535104 > 3273 [i]