Best Known (136−21, 136, s)-Nets in Base 5
(136−21, 136, 39066)-Net over F5 — Constructive and digital
Digital (115, 136, 39066)-net over F5, using
- net defined by OOA [i] based on linear OOA(5136, 39066, F5, 21, 21) (dual of [(39066, 21), 820250, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5136, 390661, F5, 21) (dual of [390661, 390525, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5136, 390664, F5, 21) (dual of [390664, 390528, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(57, 39, F5, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(5136, 390664, F5, 21) (dual of [390664, 390528, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5136, 390661, F5, 21) (dual of [390661, 390525, 22]-code), using
(136−21, 136, 195332)-Net over F5 — Digital
Digital (115, 136, 195332)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5136, 195332, F5, 2, 21) (dual of [(195332, 2), 390528, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5136, 390664, F5, 21) (dual of [390664, 390528, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(57, 39, F5, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(5136, 390664, F5, 21) (dual of [390664, 390528, 22]-code), using
(136−21, 136, large)-Net in Base 5 — Upper bound on s
There is no (115, 136, large)-net in base 5, because
- 19 times m-reduction [i] would yield (115, 117, large)-net in base 5, but