Best Known (41−11, 41, s)-Nets in Base 16
(41−11, 41, 13107)-Net over F16 — Constructive and digital
Digital (30, 41, 13107)-net over F16, using
- net defined by OOA [i] based on linear OOA(1641, 13107, F16, 11, 11) (dual of [(13107, 11), 144136, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(1641, 65536, F16, 11) (dual of [65536, 65495, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(1641, 65536, F16, 11) (dual of [65536, 65495, 12]-code), using
(41−11, 41, 62126)-Net over F16 — Digital
Digital (30, 41, 62126)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1641, 62126, F16, 11) (dual of [62126, 62085, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(1641, 65536, F16, 11) (dual of [65536, 65495, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(1641, 65536, F16, 11) (dual of [65536, 65495, 12]-code), using
(41−11, 41, large)-Net in Base 16 — Upper bound on s
There is no (30, 41, large)-net in base 16, because
- 9 times m-reduction [i] would yield (30, 32, large)-net in base 16, but