Best Known (39, 39+20, s)-Nets in Base 27
(39, 39+20, 1969)-Net over F27 — Constructive and digital
Digital (39, 59, 1969)-net over F27, using
- net defined by OOA [i] based on linear OOA(2759, 1969, F27, 20, 20) (dual of [(1969, 20), 39321, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 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(19) ⊂ Ce(17) [i] based on
- OA 10-folding and stacking [i] based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
(39, 39+20, 11885)-Net over F27 — Digital
Digital (39, 59, 11885)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2759, 11885, F27, 20) (dual of [11885, 11826, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 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(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
(39, 39+20, large)-Net in Base 27 — Upper bound on s
There is no (39, 59, large)-net in base 27, because
- 18 times m-reduction [i] would yield (39, 41, large)-net in base 27, but