Best Known (77, 77+30, s)-Nets in Base 25
(77, 77+30, 1108)-Net over F25 — Constructive and digital
Digital (77, 107, 1108)-net over F25, using
- 1 times m-reduction [i] based on digital (77, 108, 1108)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 19, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (58, 89, 1042)-net over F25, using
- net defined by OOA [i] based on linear OOA(2589, 1042, F25, 31, 31) (dual of [(1042, 31), 32213, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2589, 15631, F25, 31) (dual of [15631, 15542, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2589, 15632, F25, 31) (dual of [15632, 15543, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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 Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2589, 15632, F25, 31) (dual of [15632, 15543, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2589, 15631, F25, 31) (dual of [15631, 15542, 32]-code), using
- net defined by OOA [i] based on linear OOA(2589, 1042, F25, 31, 31) (dual of [(1042, 31), 32213, 32]-NRT-code), using
- digital (4, 19, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(77, 77+30, 69971)-Net over F25 — Digital
Digital (77, 107, 69971)-net over F25, using
(77, 77+30, large)-Net in Base 25 — Upper bound on s
There is no (77, 107, large)-net in base 25, because
- 28 times m-reduction [i] would yield (77, 79, large)-net in base 25, but