Best Known (24, 33, s)-Nets in Base 27
(24, 33, 132861)-Net over F27 — Constructive and digital
Digital (24, 33, 132861)-net over F27, using
- net defined by OOA [i] based on linear OOA(2733, 132861, F27, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(2733, 531441, F27, 9) (dual of [531441, 531408, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(8) ⊂ Ce(7) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
(24, 33, 454276)-Net over F27 — Digital
Digital (24, 33, 454276)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2733, 454276, F27, 9) (dual of [454276, 454243, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2733, 531441, F27, 9) (dual of [531441, 531408, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2733, 531441, F27, 9) (dual of [531441, 531408, 10]-code), using
(24, 33, large)-Net in Base 27 — Upper bound on s
There is no (24, 33, large)-net in base 27, because
- 7 times m-reduction [i] would yield (24, 26, large)-net in base 27, but