Best Known (44, 55, s)-Nets in Base 27
(44, 55, 1677720)-Net over F27 — Constructive and digital
Digital (44, 55, 1677720)-net over F27, using
- 274 times duplication [i] based on digital (40, 51, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
(44, 55, large)-Net over F27 — Digital
Digital (44, 55, large)-net over F27, using
- 1 times m-reduction [i] based on digital (44, 56, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
(44, 55, large)-Net in Base 27 — Upper bound on s
There is no (44, 55, large)-net in base 27, because
- 9 times m-reduction [i] would yield (44, 46, large)-net in base 27, but