Best Known (87−20, 87, s)-Nets in Base 25
(87−20, 87, 39088)-Net over F25 — Constructive and digital
Digital (67, 87, 39088)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (57, 77, 39062)-net over F25, using
- net defined by OOA [i] based on linear OOA(2577, 39062, F25, 20, 20) (dual of [(39062, 20), 781163, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2577, 390620, F25, 20) (dual of [390620, 390543, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2577, 390620, F25, 20) (dual of [390620, 390543, 21]-code), using
- net defined by OOA [i] based on linear OOA(2577, 39062, F25, 20, 20) (dual of [(39062, 20), 781163, 21]-NRT-code), using
- digital (0, 10, 26)-net over F25, using
(87−20, 87, 831961)-Net over F25 — Digital
Digital (67, 87, 831961)-net over F25, using
(87−20, 87, large)-Net in Base 25 — Upper bound on s
There is no (67, 87, large)-net in base 25, because
- 18 times m-reduction [i] would yield (67, 69, large)-net in base 25, but