Best Known (94, 94+35, s)-Nets in Base 16
(94, 94+35, 3855)-Net over F16 — Constructive and digital
Digital (94, 129, 3855)-net over F16, using
- net defined by OOA [i] based on linear OOA(16129, 3855, F16, 35, 35) (dual of [(3855, 35), 134796, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- OOA 17-folding and stacking with additional row [i] based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
(94, 94+35, 41077)-Net over F16 — Digital
Digital (94, 129, 41077)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16129, 41077, F16, 35) (dual of [41077, 40948, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
(94, 94+35, large)-Net in Base 16 — Upper bound on s
There is no (94, 129, large)-net in base 16, because
- 33 times m-reduction [i] would yield (94, 96, large)-net in base 16, but