Best Known (14, 34, s)-Nets in Base 49
(14, 34, 104)-Net over F49 — Constructive and digital
Digital (14, 34, 104)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (2, 22, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49 (see above)
- digital (2, 12, 52)-net over F49, using
(14, 34, 185)-Net over F49 — Digital
Digital (14, 34, 185)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4934, 185, F49, 20) (dual of [185, 151, 21]-code), using
- 82 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 14 times 0, 1, 21 times 0, 1, 30 times 0) [i] based on linear OA(4923, 92, F49, 20) (dual of [92, 69, 21]-code), using
- extended algebraic-geometric code AGe(F,71P) [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- 82 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 14 times 0, 1, 21 times 0, 1, 30 times 0) [i] based on linear OA(4923, 92, F49, 20) (dual of [92, 69, 21]-code), using
(14, 34, 52645)-Net in Base 49 — Upper bound on s
There is no (14, 34, 52646)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 2928 812140 335062 625571 119262 220355 347504 089653 483956 904001 > 4934 [i]