Best Known (60, 60+21, s)-Nets in Base 27
(60, 60+21, 53144)-Net over F27 — Constructive and digital
Digital (60, 81, 53144)-net over F27, using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on 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]
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
(60, 60+21, 324358)-Net over F27 — Digital
Digital (60, 81, 324358)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2781, 324358, F27, 21) (dual of [324358, 324277, 22]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
(60, 60+21, large)-Net in Base 27 — Upper bound on s
There is no (60, 81, large)-net in base 27, because
- 19 times m-reduction [i] would yield (60, 62, large)-net in base 27, but