Best Known (66, 101, s)-Nets in Base 25
(66, 101, 919)-Net over F25 — Constructive and digital
Digital (66, 101, 919)-net over F25, using
- 251 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
(66, 101, 9431)-Net over F25 — Digital
Digital (66, 101, 9431)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25101, 9431, F25, 35) (dual of [9431, 9330, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(25101, 15632, F25, 35) (dual of [15632, 15531, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(32) [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(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(34) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(25101, 15632, F25, 35) (dual of [15632, 15531, 36]-code), using
(66, 101, large)-Net in Base 25 — Upper bound on s
There is no (66, 101, large)-net in base 25, because
- 33 times m-reduction [i] would yield (66, 68, large)-net in base 25, but