Best Known (95−15, 95, s)-Nets in Base 4
(95−15, 95, 9366)-Net over F4 — Constructive and digital
Digital (80, 95, 9366)-net over F4, using
- 41 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(494, 9366, F4, 15, 15) (dual of [(9366, 15), 140396, 16]-NRT-code), using
(95−15, 95, 42613)-Net over F4 — Digital
Digital (80, 95, 42613)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(495, 42613, F4, 15) (dual of [42613, 42518, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(495, 65567, F4, 15) (dual of [65567, 65472, 16]-code), using
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [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(457, 65536, F4, 10) (dual of [65536, 65479, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(495, 65567, F4, 15) (dual of [65567, 65472, 16]-code), using
(95−15, 95, large)-Net in Base 4 — Upper bound on s
There is no (80, 95, large)-net in base 4, because
- 13 times m-reduction [i] would yield (80, 82, large)-net in base 4, but