Best Known (109−30, 109, s)-Nets in Base 25
(109−30, 109, 1145)-Net over F25 — Constructive and digital
Digital (79, 109, 1145)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (55, 85, 1041)-net over F25, using
- net defined by OOA [i] based on linear OOA(2585, 1041, F25, 30, 30) (dual of [(1041, 30), 31145, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2585, 15615, F25, 30) (dual of [15615, 15530, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2585, 15615, F25, 30) (dual of [15615, 15530, 31]-code), using
- net defined by OOA [i] based on linear OOA(2585, 1041, F25, 30, 30) (dual of [(1041, 30), 31145, 31]-NRT-code), using
- digital (9, 24, 104)-net over F25, using
(109−30, 109, 87359)-Net over F25 — Digital
Digital (79, 109, 87359)-net over F25, using
(109−30, 109, large)-Net in Base 25 — Upper bound on s
There is no (79, 109, large)-net in base 25, because
- 28 times m-reduction [i] would yield (79, 81, large)-net in base 25, but