Best Known (46−13, 46, s)-Nets in Base 25
(46−13, 46, 2656)-Net over F25 — Constructive and digital
Digital (33, 46, 2656)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (24, 37, 2604)-net over F25, using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- digital (3, 9, 52)-net over F25, using
(46−13, 46, 50347)-Net over F25 — Digital
Digital (33, 46, 50347)-net over F25, using
(46−13, 46, large)-Net in Base 25 — Upper bound on s
There is no (33, 46, large)-net in base 25, because
- 11 times m-reduction [i] would yield (33, 35, large)-net in base 25, but