Best Known (32, 44, s)-Nets in Base 25
(32, 44, 2670)-Net over F25 — Constructive and digital
Digital (32, 44, 2670)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 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 (22, 34, 2604)-net over F25, using
- net defined by OOA [i] based on linear OOA(2534, 2604, F25, 12, 12) (dual of [(2604, 12), 31214, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2534, 15624, F25, 12) (dual of [15624, 15590, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2534, 15624, F25, 12) (dual of [15624, 15590, 13]-code), using
- net defined by OOA [i] based on linear OOA(2534, 2604, F25, 12, 12) (dual of [(2604, 12), 31214, 13]-NRT-code), using
- digital (4, 10, 66)-net over F25, using
(32, 44, 79908)-Net over F25 — Digital
Digital (32, 44, 79908)-net over F25, using
(32, 44, large)-Net in Base 25 — Upper bound on s
There is no (32, 44, large)-net in base 25, because
- 10 times m-reduction [i] would yield (32, 34, large)-net in base 25, but