Best Known (72−20, 72, s)-Nets in Base 25
(72−20, 72, 1628)-Net over F25 — Constructive and digital
Digital (52, 72, 1628)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 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, 58, 1562)-net over F25, using
- net defined by OOA [i] based on linear OOA(2558, 1562, F25, 20, 20) (dual of [(1562, 20), 31182, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2558, 15620, F25, 20) (dual of [15620, 15562, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2558, 15620, F25, 20) (dual of [15620, 15562, 21]-code), using
- net defined by OOA [i] based on linear OOA(2558, 1562, F25, 20, 20) (dual of [(1562, 20), 31182, 21]-NRT-code), using
- digital (4, 14, 66)-net over F25, using
(72−20, 72, 65543)-Net over F25 — Digital
Digital (52, 72, 65543)-net over F25, using
(72−20, 72, large)-Net in Base 25 — Upper bound on s
There is no (52, 72, large)-net in base 25, because
- 18 times m-reduction [i] would yield (52, 54, large)-net in base 25, but