Best Known (16, 16+6, s)-Nets in Base 25
(16, 16+6, 130211)-Net over F25 — Constructive and digital
Digital (16, 22, 130211)-net over F25, using
- net defined by OOA [i] based on linear OOA(2522, 130211, F25, 6, 6) (dual of [(130211, 6), 781244, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2522, 390633, F25, 6) (dual of [390633, 390611, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2522, 390634, F25, 6) (dual of [390634, 390612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 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(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(2522, 390634, F25, 6) (dual of [390634, 390612, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(2522, 390633, F25, 6) (dual of [390633, 390611, 7]-code), using
(16, 16+6, 390635)-Net over F25 — Digital
Digital (16, 22, 390635)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2522, 390635, F25, 6) (dual of [390635, 390613, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(259, 10, F25, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
- dual of repetition code with length 10 [i]
- linear OA(251, 10, F25, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
(16, 16+6, large)-Net in Base 25 — Upper bound on s
There is no (16, 22, large)-net in base 25, because
- 4 times m-reduction [i] would yield (16, 18, large)-net in base 25, but