Best Known (65, 98, s)-Nets in Base 25
(65, 98, 977)-Net over F25 — Constructive and digital
Digital (65, 98, 977)-net over F25, using
- 252 times duplication [i] based on digital (63, 96, 977)-net over F25, using
- net defined by OOA [i] based on linear OOA(2596, 977, F25, 33, 33) (dual of [(977, 33), 32145, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2596, 15633, F25, 33) (dual of [15633, 15537, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, 15636, F25, 33) (dual of [15636, 15540, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
- 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(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(32) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(2596, 15636, F25, 33) (dual of [15636, 15540, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2596, 15633, F25, 33) (dual of [15633, 15537, 34]-code), using
- net defined by OOA [i] based on linear OOA(2596, 977, F25, 33, 33) (dual of [(977, 33), 32145, 34]-NRT-code), using
(65, 98, 12231)-Net over F25 — Digital
Digital (65, 98, 12231)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2598, 12231, F25, 33) (dual of [12231, 12133, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2598, 15633, F25, 33) (dual of [15633, 15535, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(2597, 15626, F25, 33) (dual of [15626, 15529, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2591, 15626, F25, 31) (dual of [15626, 15535, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [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 C([0,16]) ⊂ C([0,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2598, 15633, F25, 33) (dual of [15633, 15535, 34]-code), using
(65, 98, large)-Net in Base 25 — Upper bound on s
There is no (65, 98, large)-net in base 25, because
- 31 times m-reduction [i] would yield (65, 67, large)-net in base 25, but