Best Known (83−28, 83, s)-Nets in Base 25
(83−28, 83, 1117)-Net over F25 — Constructive and digital
Digital (55, 83, 1117)-net over F25, using
- net defined by OOA [i] based on linear OOA(2583, 1117, F25, 28, 28) (dual of [(1117, 28), 31193, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2583, 15638, F25, 28) (dual of [15638, 15555, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2583, 15641, F25, 28) (dual of [15641, 15558, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(254, 16, F25, 4) (dual of [16, 12, 5]-code or 16-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(27) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2583, 15641, F25, 28) (dual of [15641, 15558, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2583, 15638, F25, 28) (dual of [15638, 15555, 29]-code), using
(83−28, 83, 11258)-Net over F25 — Digital
Digital (55, 83, 11258)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2583, 11258, F25, 28) (dual of [11258, 11175, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2583, 15641, F25, 28) (dual of [15641, 15558, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(254, 16, F25, 4) (dual of [16, 12, 5]-code or 16-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(27) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2583, 15641, F25, 28) (dual of [15641, 15558, 29]-code), using
(83−28, 83, large)-Net in Base 25 — Upper bound on s
There is no (55, 83, large)-net in base 25, because
- 26 times m-reduction [i] would yield (55, 57, large)-net in base 25, but