Best Known (73−13, 73, s)-Nets in Base 4
(73−13, 73, 10922)-Net over F4 — Constructive and digital
Digital (60, 73, 10922)-net over F4, using
- net defined by OOA [i] based on linear OOA(473, 10922, F4, 13, 13) (dual of [(10922, 13), 141913, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(473, 65533, F4, 13) (dual of [65533, 65460, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(473, 65533, F4, 13) (dual of [65533, 65460, 14]-code), using
(73−13, 73, 28403)-Net over F4 — Digital
Digital (60, 73, 28403)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(473, 28403, F4, 2, 13) (dual of [(28403, 2), 56733, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(473, 32768, F4, 2, 13) (dual of [(32768, 2), 65463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 2-folding [i] based on linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(473, 32768, F4, 2, 13) (dual of [(32768, 2), 65463, 14]-NRT-code), using
(73−13, 73, large)-Net in Base 4 — Upper bound on s
There is no (60, 73, large)-net in base 4, because
- 11 times m-reduction [i] would yield (60, 62, large)-net in base 4, but