Best Known (54, 54+22, s)-Nets in Base 32
(54, 54+22, 3023)-Net over F32 — Constructive and digital
Digital (54, 76, 3023)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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
- digital (42, 64, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
- digital (1, 12, 44)-net over F32, using
(54, 54+22, 5959)-Net in Base 32 — Constructive
(54, 76, 5959)-net in base 32, using
- net defined by OOA [i] based on OOA(3276, 5959, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3276, 65549, S32, 22), using
- discarding factors based on OA(3276, 65550, S32, 22), using
- discarding parts of the base [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding parts of the base [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- discarding factors based on OA(3276, 65550, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3276, 65549, S32, 22), using
(54, 54+22, 78415)-Net over F32 — Digital
Digital (54, 76, 78415)-net over F32, using
(54, 54+22, large)-Net in Base 32 — Upper bound on s
There is no (54, 76, large)-net in base 32, because
- 20 times m-reduction [i] would yield (54, 56, large)-net in base 32, but