Best Known (29−12, 29, s)-Nets in Base 49
(29−12, 29, 450)-Net over F49 — Constructive and digital
Digital (17, 29, 450)-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 (11, 23, 400)-net over F49, using
- net defined by OOA [i] based on linear OOA(4923, 400, F49, 12, 12) (dual of [(400, 12), 4777, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4923, 2400, F49, 12) (dual of [2400, 2377, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4923, 2400, F49, 12) (dual of [2400, 2377, 13]-code), using
- net defined by OOA [i] based on linear OOA(4923, 400, F49, 12, 12) (dual of [(400, 12), 4777, 13]-NRT-code), using
- digital (0, 6, 50)-net over F49, using
(29−12, 29, 3118)-Net over F49 — Digital
Digital (17, 29, 3118)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4929, 3118, F49, 12) (dual of [3118, 3089, 13]-code), using
- 709 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 41 times 0, 1, 162 times 0, 1, 496 times 0) [i] based on linear OA(4923, 2403, F49, 12) (dual of [2403, 2380, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 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(11) ⊂ Ce(10) [i] based on
- 709 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 41 times 0, 1, 162 times 0, 1, 496 times 0) [i] based on linear OA(4923, 2403, F49, 12) (dual of [2403, 2380, 13]-code), using
(29−12, 29, large)-Net in Base 49 — Upper bound on s
There is no (17, 29, large)-net in base 49, because
- 10 times m-reduction [i] would yield (17, 19, large)-net in base 49, but