Best Known (110−36, 110, s)-Nets in Base 27
(110−36, 110, 1095)-Net over F27 — Constructive and digital
Digital (74, 110, 1095)-net over F27, using
- 271 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(27109, 1095, F27, 36, 36) (dual of [(1095, 36), 39311, 37]-NRT-code), using
(110−36, 110, 19712)-Net over F27 — Digital
Digital (74, 110, 19712)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27110, 19712, F27, 36) (dual of [19712, 19602, 37]-code), using
- construction XX applied to Ce(35) ⊂ Ce(28) ⊂ Ce(27) [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(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(276, 28, F27, 6) (dual of [28, 22, 7]-code or 28-arc in PG(5,27)), using
- extended Reed–Solomon code RSe(22,27) [i]
- linear OA(270, 1, F27, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(35) ⊂ Ce(28) ⊂ Ce(27) [i] based on
(110−36, 110, large)-Net in Base 27 — Upper bound on s
There is no (74, 110, large)-net in base 27, because
- 34 times m-reduction [i] would yield (74, 76, large)-net in base 27, but