Best Known (64, 86, s)-Nets in Base 27
(64, 86, 48313)-Net over F27 — Constructive and digital
Digital (64, 86, 48313)-net over F27, using
- 271 times duplication [i] based on digital (63, 85, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
(64, 86, 386917)-Net over F27 — Digital
Digital (64, 86, 386917)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2786, 386917, F27, 22) (dual of [386917, 386831, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2786, 531450, F27, 22) (dual of [531450, 531364, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2786, 531450, F27, 22) (dual of [531450, 531364, 23]-code), using
(64, 86, large)-Net in Base 27 — Upper bound on s
There is no (64, 86, large)-net in base 27, because
- 20 times m-reduction [i] would yield (64, 66, large)-net in base 27, but