Best Known (71, 71+26, s)-Nets in Base 16
(71, 71+26, 5041)-Net over F16 — Constructive and digital
Digital (71, 97, 5041)-net over F16, using
- net defined by OOA [i] based on linear OOA(1697, 5041, F16, 26, 26) (dual of [(5041, 26), 130969, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(1697, 65533, F16, 26) (dual of [65533, 65436, 27]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(1697, 65533, F16, 26) (dual of [65533, 65436, 27]-code), using
(71, 71+26, 42818)-Net over F16 — Digital
Digital (71, 97, 42818)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 42818, F16, 26) (dual of [42818, 42721, 27]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using
(71, 71+26, large)-Net in Base 16 — Upper bound on s
There is no (71, 97, large)-net in base 16, because
- 24 times m-reduction [i] would yield (71, 73, large)-net in base 16, but