Best Known (63, 84, s)-Nets in Base 16
(63, 84, 13108)-Net over F16 — Constructive and digital
Digital (63, 84, 13108)-net over F16, using
- net defined by OOA [i] based on linear OOA(1684, 13108, F16, 21, 21) (dual of [(13108, 21), 275184, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1684, 131081, F16, 21) (dual of [131081, 130997, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code), using
- trace code [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,10]) ⊂ C([0,9]) [i] based on
- trace code [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1684, 131081, F16, 21) (dual of [131081, 130997, 22]-code), using
(63, 84, 96202)-Net over F16 — Digital
Digital (63, 84, 96202)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1684, 96202, F16, 21) (dual of [96202, 96118, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code), using
- trace code [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,10]) ⊂ C([0,9]) [i] based on
- trace code [i] based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code), using
(63, 84, large)-Net in Base 16 — Upper bound on s
There is no (63, 84, large)-net in base 16, because
- 19 times m-reduction [i] would yield (63, 65, large)-net in base 16, but