Best Known (70−19, 70, s)-Nets in Base 25
(70−19, 70, 1803)-Net over F25 — Constructive and digital
Digital (51, 70, 1803)-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 (38, 57, 1737)-net over F25, using
- net defined by OOA [i] based on linear OOA(2557, 1737, F25, 19, 19) (dual of [(1737, 19), 32946, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2557, 15634, F25, 19) (dual of [15634, 15577, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2557, 15636, F25, 19) (dual of [15636, 15579, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(2557, 15636, F25, 19) (dual of [15636, 15579, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2557, 15634, F25, 19) (dual of [15634, 15577, 20]-code), using
- net defined by OOA [i] based on linear OOA(2557, 1737, F25, 19, 19) (dual of [(1737, 19), 32946, 20]-NRT-code), using
- digital (4, 13, 66)-net over F25, using
(70−19, 70, 85980)-Net over F25 — Digital
Digital (51, 70, 85980)-net over F25, using
(70−19, 70, large)-Net in Base 25 — Upper bound on s
There is no (51, 70, large)-net in base 25, because
- 17 times m-reduction [i] would yield (51, 53, large)-net in base 25, but