Best Known (67, 67+30, s)-Nets in Base 27
(67, 67+30, 1315)-Net over F27 — Constructive and digital
Digital (67, 97, 1315)-net over F27, using
- net defined by OOA [i] based on linear OOA(2797, 1315, F27, 30, 30) (dual of [(1315, 30), 39353, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2797, 19725, F27, 30) (dual of [19725, 19628, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(18) [i] based on
- linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2755, 19683, F27, 19) (dual of [19683, 19628, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2712, 42, F27, 10) (dual of [42, 30, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2712, 48, F27, 10) (dual of [48, 36, 11]-code), using
- extended algebraic-geometric code AGe(F,37P) [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- discarding factors / shortening the dual code based on linear OA(2712, 48, F27, 10) (dual of [48, 36, 11]-code), using
- construction X applied to Ce(29) ⊂ Ce(18) [i] based on
- OA 15-folding and stacking [i] based on linear OA(2797, 19725, F27, 30) (dual of [19725, 19628, 31]-code), using
(67, 67+30, 27545)-Net over F27 — Digital
Digital (67, 97, 27545)-net over F27, using
(67, 67+30, large)-Net in Base 27 — Upper bound on s
There is no (67, 97, large)-net in base 27, because
- 28 times m-reduction [i] would yield (67, 69, large)-net in base 27, but