Best Known (17, 17+18, s)-Nets in Base 25
(17, 17+18, 132)-Net over F25 — Constructive and digital
Digital (17, 35, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 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 (4, 22, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 13, 66)-net over F25, using
(17, 17+18, 311)-Net over F25 — Digital
Digital (17, 35, 311)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2535, 311, F25, 2, 18) (dual of [(311, 2), 587, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2535, 314, F25, 2, 18) (dual of [(314, 2), 593, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2535, 628, F25, 18) (dual of [628, 593, 19]-code), using
- construction XX applied to C1 = C([623,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([623,16]) [i] based on
- linear OA(2533, 624, F25, 17) (dual of [624, 591, 18]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2533, 624, F25, 17) (dual of [624, 591, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2535, 624, F25, 18) (dual of [624, 589, 19]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2531, 624, F25, 16) (dual of [624, 593, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([623,16]) [i] based on
- OOA 2-folding [i] based on linear OA(2535, 628, F25, 18) (dual of [628, 593, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(2535, 314, F25, 2, 18) (dual of [(314, 2), 593, 19]-NRT-code), using
(17, 17+18, 47199)-Net in Base 25 — Upper bound on s
There is no (17, 35, 47200)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 8 471852 782212 552094 335584 909922 800766 599923 810561 > 2535 [i]