Best Known (118−30, 118, s)-Nets in Base 16
(118−30, 118, 8738)-Net over F16 — Constructive and digital
Digital (88, 118, 8738)-net over F16, using
- net defined by OOA [i] based on linear OOA(16118, 8738, F16, 30, 30) (dual of [(8738, 30), 262022, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16118, 131070, F16, 30) (dual of [131070, 130952, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16118, 131072, F16, 30) (dual of [131072, 130954, 31]-code), using
- trace code [i] based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- trace code [i] based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16118, 131072, F16, 30) (dual of [131072, 130954, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(16118, 131070, F16, 30) (dual of [131070, 130952, 31]-code), using
(118−30, 118, 80972)-Net over F16 — Digital
Digital (88, 118, 80972)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16118, 80972, F16, 30) (dual of [80972, 80854, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16118, 131072, F16, 30) (dual of [131072, 130954, 31]-code), using
- trace code [i] based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- trace code [i] based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16118, 131072, F16, 30) (dual of [131072, 130954, 31]-code), using
(118−30, 118, large)-Net in Base 16 — Upper bound on s
There is no (88, 118, large)-net in base 16, because
- 28 times m-reduction [i] would yield (88, 90, large)-net in base 16, but