Best Known (102−35, 102, s)-Nets in Base 25
(102−35, 102, 919)-Net over F25 — Constructive and digital
Digital (67, 102, 919)-net over F25, using
- 252 times duplication [i] based on digital (65, 100, 919)-net over F25, using
- net defined by OOA [i] based on linear OOA(25100, 919, F25, 35, 35) (dual of [(919, 35), 32065, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(25100, 15624, F25, 35) (dual of [15624, 15524, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(25100, 15624, F25, 35) (dual of [15624, 15524, 36]-code), using
- net defined by OOA [i] based on linear OOA(25100, 919, F25, 35, 35) (dual of [(919, 35), 32065, 36]-NRT-code), using
(102−35, 102, 10399)-Net over F25 — Digital
Digital (67, 102, 10399)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25102, 10399, F25, 35) (dual of [10399, 10297, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(25102, 15636, F25, 35) (dual of [15636, 15534, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(31) [i] based on
- linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(34) ⊂ Ce(31) [i] based on
- discarding factors / shortening the dual code based on linear OA(25102, 15636, F25, 35) (dual of [15636, 15534, 36]-code), using
(102−35, 102, large)-Net in Base 25 — Upper bound on s
There is no (67, 102, large)-net in base 25, because
- 33 times m-reduction [i] would yield (67, 69, large)-net in base 25, but