Best Known (117−30, 117, s)-Nets in Base 16
(117−30, 117, 4370)-Net over F16 — Constructive and digital
Digital (87, 117, 4370)-net over F16, using
- 162 times duplication [i] based on digital (85, 115, 4370)-net over F16, using
- net defined by OOA [i] based on linear OOA(16115, 4370, F16, 30, 30) (dual of [(4370, 30), 130985, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- OA 15-folding and stacking [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- net defined by OOA [i] based on linear OOA(16115, 4370, F16, 30, 30) (dual of [(4370, 30), 130985, 31]-NRT-code), using
(117−30, 117, 65556)-Net over F16 — Digital
Digital (87, 117, 65556)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16117, 65556, F16, 30) (dual of [65556, 65439, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(164, 20, F16, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,16)), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
(117−30, 117, large)-Net in Base 16 — Upper bound on s
There is no (87, 117, large)-net in base 16, because
- 28 times m-reduction [i] would yield (87, 89, large)-net in base 16, but