Best Known (32, 32+22, s)-Nets in Base 128
(32, 32+22, 1618)-Net over F128 — Constructive and digital
Digital (32, 54, 1618)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (21, 43, 1489)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 1489, F128, 22, 22) (dual of [(1489, 22), 32715, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
- net defined by OOA [i] based on linear OOA(12843, 1489, F128, 22, 22) (dual of [(1489, 22), 32715, 23]-NRT-code), using
- digital (0, 11, 129)-net over F128, using
(32, 32+22, 5959)-Net in Base 128 — Constructive
(32, 54, 5959)-net in base 128, using
- net defined by OOA [i] based on OOA(12854, 5959, S128, 22, 22), using
- OA 11-folding and stacking [i] based on OA(12854, 65549, S128, 22), using
- discarding factors based on OA(12854, 65550, S128, 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(12854, 65550, S128, 22), using
- OA 11-folding and stacking [i] based on OA(12854, 65549, S128, 22), using
(32, 32+22, 17926)-Net over F128 — Digital
Digital (32, 54, 17926)-net over F128, using
(32, 32+22, large)-Net in Base 128 — Upper bound on s
There is no (32, 54, large)-net in base 128, because
- 20 times m-reduction [i] would yield (32, 34, large)-net in base 128, but