Best Known (73, 73+24, s)-Nets in Base 27
(73, 73+24, 44288)-Net over F27 — Constructive and digital
Digital (73, 97, 44288)-net over F27, using
- 271 times duplication [i] based on digital (72, 96, 44288)-net over F27, using
- net defined by OOA [i] based on linear OOA(2796, 44288, F27, 24, 24) (dual of [(44288, 24), 1062816, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2796, 531456, F27, 24) (dual of [531456, 531360, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2796, 531460, F27, 24) (dual of [531460, 531364, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(273, 19, F27, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,27) or 19-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2796, 531460, F27, 24) (dual of [531460, 531364, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2796, 531456, F27, 24) (dual of [531456, 531360, 25]-code), using
- net defined by OOA [i] based on linear OOA(2796, 44288, F27, 24, 24) (dual of [(44288, 24), 1062816, 25]-NRT-code), using
(73, 73+24, 531465)-Net over F27 — Digital
Digital (73, 97, 531465)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2797, 531465, F27, 24) (dual of [531465, 531368, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2773, 531441, F27, 19) (dual of [531441, 531368, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(274, 24, F27, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- construction X applied to Ce(23) ⊂ Ce(18) [i] based on
(73, 73+24, large)-Net in Base 27 — Upper bound on s
There is no (73, 97, large)-net in base 27, because
- 22 times m-reduction [i] would yield (73, 75, large)-net in base 27, but