Best Known (28, 43, s)-Nets in Base 128
(28, 43, 299593)-Net over F128 — Constructive and digital
Digital (28, 43, 299593)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 299593, F128, 15, 15) (dual of [(299593, 15), 4493852, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using
(28, 43, 699051)-Net over F128 — Digital
Digital (28, 43, 699051)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12843, 699051, F128, 3, 15) (dual of [(699051, 3), 2097110, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using
(28, 43, large)-Net in Base 128 — Upper bound on s
There is no (28, 43, large)-net in base 128, because
- 13 times m-reduction [i] would yield (28, 30, large)-net in base 128, but