Best Known (101−22, 101, s)-Nets in Base 16
(101−22, 101, 95325)-Net over F16 — Constructive and digital
Digital (79, 101, 95325)-net over F16, using
- net defined by OOA [i] based on linear OOA(16101, 95325, F16, 22, 22) (dual of [(95325, 22), 2097049, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16101, 1048575, F16, 22) (dual of [1048575, 1048474, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16101, 1048575, F16, 22) (dual of [1048575, 1048474, 23]-code), using
(101−22, 101, 580507)-Net over F16 — Digital
Digital (79, 101, 580507)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16101, 580507, F16, 22) (dual of [580507, 580406, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using
(101−22, 101, large)-Net in Base 16 — Upper bound on s
There is no (79, 101, large)-net in base 16, because
- 20 times m-reduction [i] would yield (79, 81, large)-net in base 16, but