Best Known (93, 124, s)-Nets in Base 16
(93, 124, 8738)-Net over F16 — Constructive and digital
Digital (93, 124, 8738)-net over F16, using
- 162 times duplication [i] based on digital (91, 122, 8738)-net over F16, using
- net defined by OOA [i] based on linear OOA(16122, 8738, F16, 31, 31) (dual of [(8738, 31), 270756, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16122, 131071, F16, 31) (dual of [131071, 130949, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16122, 131074, F16, 31) (dual of [131074, 130952, 32]-code), using
- trace code [i] based on linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- trace code [i] based on linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16122, 131074, F16, 31) (dual of [131074, 130952, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16122, 131071, F16, 31) (dual of [131071, 130949, 32]-code), using
- net defined by OOA [i] based on linear OOA(16122, 8738, F16, 31, 31) (dual of [(8738, 31), 270756, 32]-NRT-code), using
(93, 124, 99562)-Net over F16 — Digital
Digital (93, 124, 99562)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16124, 99562, F16, 31) (dual of [99562, 99438, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16124, 131084, F16, 31) (dual of [131084, 130960, 32]-code), using
- trace code [i] based on linear OA(25662, 65542, F256, 31) (dual of [65542, 65480, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- trace code [i] based on linear OA(25662, 65542, F256, 31) (dual of [65542, 65480, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16124, 131084, F16, 31) (dual of [131084, 130960, 32]-code), using
(93, 124, large)-Net in Base 16 — Upper bound on s
There is no (93, 124, large)-net in base 16, because
- 29 times m-reduction [i] would yield (93, 95, large)-net in base 16, but