Best Known (73−30, 73, s)-Nets in Base 128
(73−30, 73, 1095)-Net over F128 — Constructive and digital
Digital (43, 73, 1095)-net over F128, using
- 1 times m-reduction [i] based on digital (43, 74, 1095)-net over F128, using
- net defined by OOA [i] based on linear OOA(12874, 1095, F128, 31, 31) (dual of [(1095, 31), 33871, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12874, 16426, F128, 31) (dual of [16426, 16352, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,8]) [i] based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12813, 41, F128, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,128)), using
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
- Reed–Solomon code RS(115,128) [i]
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
- construction X applied to C([0,15]) ⊂ C([0,8]) [i] based on
- OOA 15-folding and stacking with additional row [i] based on linear OA(12874, 16426, F128, 31) (dual of [16426, 16352, 32]-code), using
- net defined by OOA [i] based on linear OOA(12874, 1095, F128, 31, 31) (dual of [(1095, 31), 33871, 32]-NRT-code), using
(73−30, 73, 4370)-Net in Base 128 — Constructive
(43, 73, 4370)-net in base 128, using
- 1281 times duplication [i] based on (42, 72, 4370)-net in base 128, using
- base change [i] based on digital (33, 63, 4370)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(29) ⊂ Ce(24) [i] based on
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
- base change [i] based on digital (33, 63, 4370)-net over F256, using
(73−30, 73, 18536)-Net over F128 — Digital
Digital (43, 73, 18536)-net over F128, using
(73−30, 73, large)-Net in Base 128 — Upper bound on s
There is no (43, 73, large)-net in base 128, because
- 28 times m-reduction [i] would yield (43, 45, large)-net in base 128, but