Best Known (21, 30, s)-Nets in Base 128
(21, 30, 524438)-Net over F128 — Constructive and digital
Digital (21, 30, 524438)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (16, 25, 524288)-net over F128, using
- net defined by OOA [i] based on linear OOA(12825, 524288, F128, 9, 9) (dual of [(524288, 9), 4718567, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using
- net defined by OOA [i] based on linear OOA(12825, 524288, F128, 9, 9) (dual of [(524288, 9), 4718567, 10]-NRT-code), using
- digital (1, 5, 150)-net over F128, using
(21, 30, 2097150)-Net in Base 128 — Constructive
(21, 30, 2097150)-net in base 128, using
- 1281 times duplication [i] based on (20, 29, 2097150)-net in base 128, using
- net defined by OOA [i] based on OOA(12829, 2097150, S128, 9, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(12829, 8388601, S128, 9), using
- discarding factors based on OA(12829, large, S128, 9), using
- discarding parts of the base [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding parts of the base [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- discarding factors based on OA(12829, large, S128, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(12829, 8388601, S128, 9), using
- net defined by OOA [i] based on OOA(12829, 2097150, S128, 9, 9), using
(21, 30, 2365508)-Net over F128 — Digital
Digital (21, 30, 2365508)-net over F128, using
(21, 30, 5287315)-Net in Base 128
(21, 30, 5287315)-net in base 128, using
- net defined by OOA [i] based on OOA(12830, 5287315, S128, 12, 9), using
- OOA stacking with additional row [i] based on OOA(12830, 5287316, S128, 4, 9), using
- discarding parts of the base [i] based on linear OOA(25626, 5287316, F256, 4, 9) (dual of [(5287316, 4), 21149238, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25626, 5287316, F256, 9) (dual of [5287316, 5287290, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, large, F256, 9) (dual of [large, large−26, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 1 times code embedding in larger space [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, large, F256, 9) (dual of [large, large−26, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25626, 5287316, F256, 9) (dual of [5287316, 5287290, 10]-code), using
- discarding parts of the base [i] based on linear OOA(25626, 5287316, F256, 4, 9) (dual of [(5287316, 4), 21149238, 10]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12830, 5287316, S128, 4, 9), using
(21, 30, large)-Net in Base 128 — Upper bound on s
There is no (21, 30, large)-net in base 128, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 128, but