Best Known (119−18, 119, s)-Nets in Base 5
(119−18, 119, 43406)-Net over F5 — Constructive and digital
Digital (101, 119, 43406)-net over F5, using
- 51 times duplication [i] based on digital (100, 118, 43406)-net over F5, using
- net defined by OOA [i] based on linear OOA(5118, 43406, F5, 18, 18) (dual of [(43406, 18), 781190, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(5118, 390654, F5, 18) (dual of [390654, 390536, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- OA 9-folding and stacking [i] based on linear OA(5118, 390654, F5, 18) (dual of [390654, 390536, 19]-code), using
- net defined by OOA [i] based on linear OOA(5118, 43406, F5, 18, 18) (dual of [(43406, 18), 781190, 19]-NRT-code), using
(119−18, 119, 242864)-Net over F5 — Digital
Digital (101, 119, 242864)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5119, 242864, F5, 18) (dual of [242864, 242745, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5119, 390656, F5, 18) (dual of [390656, 390537, 19]-code), using
- construction XX applied to Ce(17) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(55, 30, F5, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(17) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(5119, 390656, F5, 18) (dual of [390656, 390537, 19]-code), using
(119−18, 119, large)-Net in Base 5 — Upper bound on s
There is no (101, 119, large)-net in base 5, because
- 16 times m-reduction [i] would yield (101, 103, large)-net in base 5, but