Best Known (109−36, 109, s)-Nets in Base 27
(109−36, 109, 1095)-Net over F27 — Constructive and digital
Digital (73, 109, 1095)-net over F27, using
- net defined by OOA [i] based on linear OOA(27109, 1095, F27, 36, 36) (dual of [(1095, 36), 39311, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(27109, 19710, F27, 36) (dual of [19710, 19601, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- linear OA(27103, 19683, F27, 36) (dual of [19683, 19580, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)), using
- Reed–Solomon code RS(21,27) [i]
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- OA 18-folding and stacking [i] based on linear OA(27109, 19710, F27, 36) (dual of [19710, 19601, 37]-code), using
(109−36, 109, 18314)-Net over F27 — Digital
Digital (73, 109, 18314)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27109, 18314, F27, 36) (dual of [18314, 18205, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(27109, 19710, F27, 36) (dual of [19710, 19601, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- linear OA(27103, 19683, F27, 36) (dual of [19683, 19580, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(276, 27, F27, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,27)), using
- Reed–Solomon code RS(21,27) [i]
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(27109, 19710, F27, 36) (dual of [19710, 19601, 37]-code), using
(109−36, 109, large)-Net in Base 27 — Upper bound on s
There is no (73, 109, large)-net in base 27, because
- 34 times m-reduction [i] would yield (73, 75, large)-net in base 27, but