Best Known (18, 26, s)-Nets in Base 49
(18, 26, 29463)-Net over F49 — Constructive and digital
Digital (18, 26, 29463)-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 (14, 22, 29413)-net over F49, using
- net defined by OOA [i] based on linear OOA(4922, 29413, F49, 8, 8) (dual of [(29413, 8), 235282, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4922, 117652, F49, 8) (dual of [117652, 117630, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4919, 117649, F49, 7) (dual of [117649, 117630, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(4922, 117652, F49, 8) (dual of [117652, 117630, 9]-code), using
- net defined by OOA [i] based on linear OOA(4922, 29413, F49, 8, 8) (dual of [(29413, 8), 235282, 9]-NRT-code), using
- digital (0, 4, 50)-net over F49, using
(18, 26, 133524)-Net over F49 — Digital
Digital (18, 26, 133524)-net over F49, using
(18, 26, large)-Net in Base 49 — Upper bound on s
There is no (18, 26, large)-net in base 49, because
- 6 times m-reduction [i] would yield (18, 20, large)-net in base 49, but