Best Known (28, 40, s)-Nets in Base 49
(28, 40, 19658)-Net over F49 — Constructive and digital
Digital (28, 40, 19658)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (22, 34, 19608)-net over F49, using
- net defined by OOA [i] based on linear OOA(4934, 19608, F49, 12, 12) (dual of [(19608, 12), 235262, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4934, 117648, F49, 12) (dual of [117648, 117614, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4934, 117648, F49, 12) (dual of [117648, 117614, 13]-code), using
- net defined by OOA [i] based on linear OOA(4934, 19608, F49, 12, 12) (dual of [(19608, 12), 235262, 13]-NRT-code), using
- digital (0, 6, 50)-net over F49, using
(28, 40, 143205)-Net over F49 — Digital
Digital (28, 40, 143205)-net over F49, using
(28, 40, large)-Net in Base 49 — Upper bound on s
There is no (28, 40, large)-net in base 49, because
- 10 times m-reduction [i] would yield (28, 30, large)-net in base 49, but