Best Known (143−22, 143, s)-Nets in Base 5
(143−22, 143, 35514)-Net over F5 — Constructive and digital
Digital (121, 143, 35514)-net over F5, using
- 51 times duplication [i] based on digital (120, 142, 35514)-net over F5, using
- net defined by OOA [i] based on linear OOA(5142, 35514, F5, 22, 22) (dual of [(35514, 22), 781166, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5142, 390654, F5, 22) (dual of [390654, 390512, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(5137, 390625, F5, 22) (dual of [390625, 390488, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(17) [i] based on
- OA 11-folding and stacking [i] based on linear OA(5142, 390654, F5, 22) (dual of [390654, 390512, 23]-code), using
- net defined by OOA [i] based on linear OOA(5142, 35514, F5, 22, 22) (dual of [(35514, 22), 781166, 23]-NRT-code), using
(143−22, 143, 195328)-Net over F5 — Digital
Digital (121, 143, 195328)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5143, 195328, F5, 2, 22) (dual of [(195328, 2), 390513, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5143, 390656, F5, 22) (dual of [390656, 390513, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- linear OA(5137, 390625, F5, 22) (dual of [390625, 390488, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(5105, 390625, F5, 17) (dual of [390625, 390520, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(5143, 390656, F5, 22) (dual of [390656, 390513, 23]-code), using
(143−22, 143, large)-Net in Base 5 — Upper bound on s
There is no (121, 143, large)-net in base 5, because
- 20 times m-reduction [i] would yield (121, 123, large)-net in base 5, but