Best Known (90, 90+27, s)-Nets in Base 16
(90, 90+27, 10085)-Net over F16 — Constructive and digital
Digital (90, 117, 10085)-net over F16, using
- 161 times duplication [i] based on digital (89, 116, 10085)-net over F16, using
- net defined by OOA [i] based on linear OOA(16116, 10085, F16, 27, 27) (dual of [(10085, 27), 272179, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16116, 131106, F16, 27) (dual of [131106, 130990, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16116, 131108, F16, 27) (dual of [131108, 130992, 28]-code), using
- trace code [i] based on linear OA(25658, 65554, F256, 27) (dual of [65554, 65496, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- 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(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- trace code [i] based on linear OA(25658, 65554, F256, 27) (dual of [65554, 65496, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16116, 131108, F16, 27) (dual of [131108, 130992, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16116, 131106, F16, 27) (dual of [131106, 130990, 28]-code), using
- net defined by OOA [i] based on linear OOA(16116, 10085, F16, 27, 27) (dual of [(10085, 27), 272179, 28]-NRT-code), using
(90, 90+27, 184405)-Net over F16 — Digital
Digital (90, 117, 184405)-net over F16, using
(90, 90+27, large)-Net in Base 16 — Upper bound on s
There is no (90, 117, large)-net in base 16, because
- 25 times m-reduction [i] would yield (90, 92, large)-net in base 16, but