Best Known (36, 36+11, s)-Nets in Base 128
(36, 36+11, 1677870)-Net over F128 — Constructive and digital
Digital (36, 47, 1677870)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (30, 41, 1677720)-net over F128, using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- digital (1, 6, 150)-net over F128, using
(36, 36+11, 1726873)-Net in Base 128 — Constructive
(36, 47, 1726873)-net in base 128, using
- (u, u+v)-construction [i] based on
- (6, 11, 49153)-net in base 128, using
- net defined by OOA [i] based on OOA(12811, 49153, S128, 5, 5), using
- appending kth column [i] based on OOA(12811, 49153, S128, 4, 5), using
- (u, u+v)-construction [i] based on
- linear OOA(1283, 16513, F128, 4, 2) (dual of [(16513, 4), 66049, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1283, 16513, F128, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1283, 16513, F128, 2) (dual of [16513, 16510, 3]-code), using
- Hamming code H(3,128) [i]
- appending kth column [i] based on linear OA(1283, 16513, F128, 2) (dual of [16513, 16510, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1283, 16513, F128, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
- OOA(1288, 32640, S128, 4, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(1288, 65281, S128, 5), using
- discarding parts of the base [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(1288, 65281, S128, 5), using
- linear OOA(1283, 16513, F128, 4, 2) (dual of [(16513, 4), 66049, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on OOA(12811, 49153, S128, 4, 5), using
- net defined by OOA [i] based on OOA(12811, 49153, S128, 5, 5), using
- (25, 36, 1677720)-net in base 128, using
- net defined by OOA [i] based on OOA(12836, 1677720, S128, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(12836, 8388601, S128, 11), using
- discarding factors based on OA(12836, large, S128, 11), using
- discarding parts of the base [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding parts of the base [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- discarding factors based on OA(12836, large, S128, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(12836, 8388601, S128, 11), using
- net defined by OOA [i] based on OOA(12836, 1677720, S128, 11, 11), using
- (6, 11, 49153)-net in base 128, using
(36, 36+11, large)-Net over F128 — Digital
Digital (36, 47, large)-net over F128, using
- t-expansion [i] based on digital (35, 47, large)-net over F128, using
- 1 times m-reduction [i] based on digital (35, 48, large)-net over F128, using
(36, 36+11, large)-Net in Base 128 — Upper bound on s
There is no (36, 47, large)-net in base 128, because
- 9 times m-reduction [i] would yield (36, 38, large)-net in base 128, but