Best Known (74, 88, s)-Nets in Base 5
(74, 88, 11186)-Net over F5 — Constructive and digital
Digital (74, 88, 11186)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 25)-net over F5, using
- digital (64, 78, 11161)-net over F5, using
- net defined by OOA [i] based on linear OOA(578, 11161, F5, 14, 14) (dual of [(11161, 14), 156176, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(578, 78127, F5, 14) (dual of [78127, 78049, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(578, 78132, F5, 14) (dual of [78132, 78054, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(578, 78132, F5, 14) (dual of [78132, 78054, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(578, 78127, F5, 14) (dual of [78127, 78049, 15]-code), using
- net defined by OOA [i] based on linear OOA(578, 11161, F5, 14, 14) (dual of [(11161, 14), 156176, 15]-NRT-code), using
(74, 88, 78171)-Net over F5 — Digital
Digital (74, 88, 78171)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(588, 78171, F5, 14) (dual of [78171, 78083, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(587, 78169, F5, 14) (dual of [78169, 78082, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(587, 78170, F5, 13) (dual of [78170, 78083, 14]-code), using Gilbert–Varšamov bound and bm = 587 > Vbs−1(k−1) = 1821 577160 700635 461618 895327 238024 428986 335790 612616 792869 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(587, 78169, F5, 14) (dual of [78169, 78082, 15]-code), using
- construction X with Varšamov bound [i] based on
(74, 88, large)-Net in Base 5 — Upper bound on s
There is no (74, 88, large)-net in base 5, because
- 12 times m-reduction [i] would yield (74, 76, large)-net in base 5, but