Best Known (92, 92+23, s)-Nets in Base 5
(92, 92+23, 1423)-Net over F5 — Constructive and digital
Digital (92, 115, 1423)-net over F5, using
- net defined by OOA [i] based on linear OOA(5115, 1423, F5, 23, 23) (dual of [(1423, 23), 32614, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5115, 15654, F5, 23) (dual of [15654, 15539, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15655, F5, 23) (dual of [15655, 15540, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5115, 15655, F5, 23) (dual of [15655, 15540, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5115, 15654, F5, 23) (dual of [15654, 15539, 24]-code), using
(92, 92+23, 13501)-Net over F5 — Digital
Digital (92, 115, 13501)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5115, 13501, F5, 23) (dual of [13501, 13386, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15651, F5, 23) (dual of [15651, 15536, 24]-code), using
- construction XX applied to Ce(22) ⊂ Ce(18) ⊂ Ce(17) [i] based on
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(54, 24, F5, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,5)), using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to Ce(22) ⊂ Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5115, 15651, F5, 23) (dual of [15651, 15536, 24]-code), using
(92, 92+23, large)-Net in Base 5 — Upper bound on s
There is no (92, 115, large)-net in base 5, because
- 21 times m-reduction [i] would yield (92, 94, large)-net in base 5, but