Best Known (54−16, 54, s)-Nets in Base 25
(54−16, 54, 1979)-Net over F25 — Constructive and digital
Digital (38, 54, 1979)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (30, 46, 1953)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1953, F25, 16, 16) (dual of [(1953, 16), 31202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1953, F25, 16, 16) (dual of [(1953, 16), 31202, 17]-NRT-code), using
- digital (0, 8, 26)-net over F25, using
(54−16, 54, 28857)-Net over F25 — Digital
Digital (38, 54, 28857)-net over F25, using
(54−16, 54, large)-Net in Base 25 — Upper bound on s
There is no (38, 54, large)-net in base 25, because
- 14 times m-reduction [i] would yield (38, 40, large)-net in base 25, but