Best Known (34, 34+33, s)-Nets in Base 25
(34, 34+33, 208)-Net over F25 — Constructive and digital
Digital (34, 67, 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, 42, 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
(34, 34+33, 476)-Net over F25 — Digital
Digital (34, 67, 476)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2567, 476, F25, 33) (dual of [476, 409, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2567, 642, F25, 33) (dual of [642, 575, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2562, 625, F25, 33) (dual of [625, 563, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2550, 625, F25, 27) (dual of [625, 575, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(255, 17, F25, 5) (dual of [17, 12, 6]-code or 17-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
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2567, 642, F25, 33) (dual of [642, 575, 34]-code), using
(34, 34+33, 165504)-Net in Base 25 — Upper bound on s
There is no (34, 67, 165505)-net in base 25, because
- 1 times m-reduction [i] would yield (34, 66, 165505)-net in base 25, but
- 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]