Best Known (54, 54+17, s)-Nets in Base 25
(54, 54+17, 48831)-Net over F25 — Constructive and digital
Digital (54, 71, 48831)-net over F25, using
- 252 times duplication [i] based on digital (52, 69, 48831)-net over F25, using
- net defined by OOA [i] based on linear OOA(2569, 48831, F25, 17, 17) (dual of [(48831, 17), 830058, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2569, 390649, F25, 17) (dual of [390649, 390580, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(2569, 390649, F25, 17) (dual of [390649, 390580, 18]-code), using
- net defined by OOA [i] based on linear OOA(2569, 48831, F25, 17, 17) (dual of [(48831, 17), 830058, 18]-NRT-code), using
(54, 54+17, 452578)-Net over F25 — Digital
Digital (54, 71, 452578)-net over F25, using
(54, 54+17, large)-Net in Base 25 — Upper bound on s
There is no (54, 71, large)-net in base 25, because
- 15 times m-reduction [i] would yield (54, 56, large)-net in base 25, but