Best Known (94−15, 94, s)-Nets in Base 4
(94−15, 94, 9366)-Net over F4 — Constructive and digital
Digital (79, 94, 9366)-net over F4, using
- net defined by OOA [i] based on linear OOA(494, 9366, F4, 15, 15) (dual of [(9366, 15), 140396, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(494, 65563, F4, 15) (dual of [65563, 65469, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(494, 65565, F4, 15) (dual of [65565, 65471, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(465, 65536, F4, 11) (dual of [65536, 65471, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(494, 65565, F4, 15) (dual of [65565, 65471, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(494, 65563, F4, 15) (dual of [65563, 65469, 16]-code), using
(94−15, 94, 38302)-Net over F4 — Digital
Digital (79, 94, 38302)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(494, 38302, F4, 15) (dual of [38302, 38208, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(494, 65565, F4, 15) (dual of [65565, 65471, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(465, 65536, F4, 11) (dual of [65536, 65471, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(494, 65565, F4, 15) (dual of [65565, 65471, 16]-code), using
(94−15, 94, large)-Net in Base 4 — Upper bound on s
There is no (79, 94, large)-net in base 4, because
- 13 times m-reduction [i] would yield (79, 81, large)-net in base 4, but