Best Known (66−32, 66, s)-Nets in Base 25
(66−32, 66, 208)-Net over F25 — Constructive and digital
Digital (34, 66, 208)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 25, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (9, 41, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- digital (9, 25, 104)-net over F25, using
(66−32, 66, 523)-Net over F25 — Digital
Digital (34, 66, 523)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2566, 523, F25, 32) (dual of [523, 457, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, 643, F25, 32) (dual of [643, 577, 33]-code), using
- construction XX applied to C1 = C([620,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([620,27]) [i] based on
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2549, 624, F25, 25) (dual of [624, 575, 26]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,27}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,27}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2547, 624, F25, 24) (dual of [624, 577, 25]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,26}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(256, 17, F25, 6) (dual of [17, 11, 7]-code or 17-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- 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
- construction XX applied to C1 = C([620,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([620,27]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2566, 643, F25, 32) (dual of [643, 577, 33]-code), using
(66−32, 66, 165504)-Net in Base 25 — Upper bound on s
There is no (34, 66, 165505)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 183 688105 641593 231187 773169 542736 109230 126133 438596 404101 214204 191942 937892 953907 587107 991425 > 2566 [i]