Best Known (50, 60, s)-Nets in Base 5
(50, 60, 15629)-Net over F5 — Constructive and digital
Digital (50, 60, 15629)-net over F5, using
- net defined by OOA [i] based on linear OOA(560, 15629, F5, 10, 10) (dual of [(15629, 10), 156230, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(560, 78145, F5, 10) (dual of [78145, 78085, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(560, 78149, F5, 10) (dual of [78149, 78089, 11]-code), using
- 1 times truncation [i] based on linear OA(561, 78150, F5, 11) (dual of [78150, 78089, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(561, 78150, F5, 11) (dual of [78150, 78089, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(560, 78149, F5, 10) (dual of [78149, 78089, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(560, 78145, F5, 10) (dual of [78145, 78085, 11]-code), using
(50, 60, 78149)-Net over F5 — Digital
Digital (50, 60, 78149)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(560, 78149, F5, 10) (dual of [78149, 78089, 11]-code), using
- 1 times truncation [i] based on linear OA(561, 78150, F5, 11) (dual of [78150, 78089, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(561, 78150, F5, 11) (dual of [78150, 78089, 12]-code), using
(50, 60, large)-Net in Base 5 — Upper bound on s
There is no (50, 60, large)-net in base 5, because
- 8 times m-reduction [i] would yield (50, 52, large)-net in base 5, but