Best Known (45, 73, s)-Nets in Base 128
(45, 73, 1362)-Net over F128 — Constructive and digital
Digital (45, 73, 1362)-net over F128, using
- 1 times m-reduction [i] based on digital (45, 74, 1362)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (28, 57, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12857, 1170, F128, 29, 29) (dual of [(1170, 29), 33873, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
- net defined by OOA [i] based on linear OOA(12857, 1170, F128, 29, 29) (dual of [(1170, 29), 33873, 30]-NRT-code), using
- digital (3, 17, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(45, 73, 4683)-Net in Base 128 — Constructive
(45, 73, 4683)-net in base 128, using
- 1281 times duplication [i] based on (44, 72, 4683)-net in base 128, using
- base change [i] based on digital (35, 63, 4683)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
- base change [i] based on digital (35, 63, 4683)-net over F256, using
(45, 73, 42856)-Net over F128 — Digital
Digital (45, 73, 42856)-net over F128, using
(45, 73, large)-Net in Base 128 — Upper bound on s
There is no (45, 73, large)-net in base 128, because
- 26 times m-reduction [i] would yield (45, 47, large)-net in base 128, but