Best Known (32, 63, s)-Nets in Base 25
(32, 63, 204)-Net over F25 — Constructive and digital
Digital (32, 63, 204)-net over F25, using
- t-expansion [i] based on digital (30, 63, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
(32, 63, 461)-Net over F25 — Digital
Digital (32, 63, 461)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2563, 461, F25, 31) (dual of [461, 398, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2563, 640, F25, 31) (dual of [640, 577, 32]-code), using
- construction XX applied to C1 = C([621,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([621,27]) [i] based on
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,26}, and designed minimum distance d ≥ |I|+1 = 31 [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(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 = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [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(255, 14, F25, 5) (dual of [14, 9, 6]-code or 14-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), 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([621,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([621,27]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2563, 640, F25, 31) (dual of [640, 577, 32]-code), using
(32, 63, 160578)-Net in Base 25 — Upper bound on s
There is no (32, 63, 160579)-net in base 25, because
- 1 times m-reduction [i] would yield (32, 62, 160579)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 470 229176 544694 048140 036200 952740 033152 115282 154163 873363 032719 780600 072923 387090 185145 > 2562 [i]