Best Known (33, 33+10, s)-Nets in Base 128
(33, 33+10, 1677870)-Net over F128 — Constructive and digital
Digital (33, 43, 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 (27, 37, 1677720)-net over F128, using
- net defined by OOA [i] based on linear OOA(12837, 1677720, F128, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(12837, 8388600, F128, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12837, large, F128, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(12837, large, F128, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(12837, 8388600, F128, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(12837, 1677720, F128, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- digital (1, 6, 150)-net over F128, using
(33, 33+10, 1726873)-Net in Base 128 — Constructive
(33, 43, 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
- (22, 32, 1677720)-net in base 128, using
- base change [i] based on digital (18, 28, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- base change [i] based on digital (18, 28, 1677720)-net over F256, using
- (6, 11, 49153)-net in base 128, using
(33, 33+10, large)-Net over F128 — Digital
Digital (33, 43, large)-net over F128, using
- t-expansion [i] based on digital (32, 43, large)-net over F128, using
- 1 times m-reduction [i] based on digital (32, 44, large)-net over F128, using
(33, 33+10, large)-Net in Base 128 — Upper bound on s
There is no (33, 43, large)-net in base 128, because
- 8 times m-reduction [i] would yield (33, 35, large)-net in base 128, but