Best Known (77, 93, s)-Nets in Base 25
(77, 93, 1048733)-Net over F25 — Constructive and digital
Digital (77, 93, 1048733)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 17, 158)-net over F25, using
- net defined by OOA [i] based on linear OOA(2517, 158, F25, 8, 8) (dual of [(158, 8), 1247, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2517, 632, F25, 8) (dual of [632, 615, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2517, 633, F25, 8) (dual of [633, 616, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(2515, 625, F25, 8) (dual of [625, 610, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(259, 625, F25, 5) (dual of [625, 616, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-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(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2517, 633, F25, 8) (dual of [633, 616, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2517, 632, F25, 8) (dual of [632, 615, 9]-code), using
- net defined by OOA [i] based on linear OOA(2517, 158, F25, 8, 8) (dual of [(158, 8), 1247, 9]-NRT-code), using
- digital (60, 76, 1048575)-net over F25, using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (9, 17, 158)-net over F25, using
(77, 93, large)-Net over F25 — Digital
Digital (77, 93, large)-net over F25, using
- 4 times m-reduction [i] based on digital (77, 97, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2597, large, F25, 20) (dual of [large, large−97, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2597, large, F25, 20) (dual of [large, large−97, 21]-code), using
(77, 93, large)-Net in Base 25 — Upper bound on s
There is no (77, 93, large)-net in base 25, because
- 14 times m-reduction [i] would yield (77, 79, large)-net in base 25, but