Best Known (76, 76+11, s)-Nets in Base 3
(76, 76+11, 106291)-Net over F3 — Constructive and digital
Digital (76, 87, 106291)-net over F3, using
- net defined by OOA [i] based on linear OOA(387, 106291, F3, 11, 11) (dual of [(106291, 11), 1169114, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(387, 531456, F3, 11) (dual of [531456, 531369, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(386, 531455, F3, 11) (dual of [531455, 531369, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(386, 531455, F3, 11) (dual of [531455, 531369, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(387, 531456, F3, 11) (dual of [531456, 531369, 12]-code), using
(76, 76+11, 220831)-Net over F3 — Digital
Digital (76, 87, 220831)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(387, 220831, F3, 2, 11) (dual of [(220831, 2), 441575, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(387, 265728, F3, 2, 11) (dual of [(265728, 2), 531369, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(387, 531456, F3, 11) (dual of [531456, 531369, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(386, 531455, F3, 11) (dual of [531455, 531369, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(386, 531455, F3, 11) (dual of [531455, 531369, 12]-code), using
- OOA 2-folding [i] based on linear OA(387, 531456, F3, 11) (dual of [531456, 531369, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(387, 265728, F3, 2, 11) (dual of [(265728, 2), 531369, 12]-NRT-code), using
(76, 76+11, large)-Net in Base 3 — Upper bound on s
There is no (76, 87, large)-net in base 3, because
- 9 times m-reduction [i] would yield (76, 78, large)-net in base 3, but