Best Known (21, 30, s)-Nets in Base 49
(21, 30, 29464)-Net over F49 — Constructive and digital
Digital (21, 30, 29464)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (17, 26, 29414)-net over F49, using
- net defined by OOA [i] based on linear OOA(4926, 29414, F49, 9, 9) (dual of [(29414, 9), 264700, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4926, 117657, F49, 9) (dual of [117657, 117631, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(4925, 117650, F49, 9) (dual of [117650, 117625, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(4919, 117650, F49, 7) (dual of [117650, 117631, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(4926, 117657, F49, 9) (dual of [117657, 117631, 10]-code), using
- net defined by OOA [i] based on linear OOA(4926, 29414, F49, 9, 9) (dual of [(29414, 9), 264700, 10]-NRT-code), using
- digital (0, 4, 50)-net over F49, using
(21, 30, 170881)-Net over F49 — Digital
Digital (21, 30, 170881)-net over F49, using
(21, 30, large)-Net in Base 49 — Upper bound on s
There is no (21, 30, large)-net in base 49, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 49, but