Best Known (31−18, 31, s)-Nets in Base 49
(31−18, 31, 104)-Net over F49 — Constructive and digital
Digital (13, 31, 104)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (2, 20, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49 (see above)
- digital (2, 11, 52)-net over F49, using
(31−18, 31, 202)-Net over F49 — Digital
Digital (13, 31, 202)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4931, 202, F49, 18) (dual of [202, 171, 19]-code), using
- construction X applied to C([16,33]) ⊂ C([17,33]) [i] based on
- linear OA(4931, 200, F49, 18) (dual of [200, 169, 19]-code), using the BCH-code C(I) with length 200 | 492−1, defining interval I = {16,17,…,33}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4929, 200, F49, 17) (dual of [200, 171, 18]-code), using the BCH-code C(I) with length 200 | 492−1, defining interval I = {17,18,…,33}, and designed minimum distance d ≥ |I|+1 = 18 [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 C([16,33]) ⊂ C([17,33]) [i] based on
(31−18, 31, 57314)-Net in Base 49 — Upper bound on s
There is no (13, 31, 57315)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 24894 782104 298405 406740 993514 868058 679601 661391 611665 > 4931 [i]