Best Known (15, 37, s)-Nets in Base 49
(15, 37, 104)-Net over F49 — Constructive and digital
Digital (15, 37, 104)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (2, 24, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49 (see above)
- digital (2, 13, 52)-net over F49, using
(15, 37, 183)-Net over F49 — Digital
Digital (15, 37, 183)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4937, 183, F49, 22) (dual of [183, 146, 23]-code), using
- 92 step Varšamov–Edel lengthening with (ri) = (7, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 16 times 0, 1, 22 times 0, 1, 27 times 0) [i] based on linear OA(4924, 78, F49, 22) (dual of [78, 54, 23]-code), using
- extended algebraic-geometric code AGe(F,55P) [i] based on function field F/F49 with g(F) = 2 and N(F) ≥ 78, using
- 92 step Varšamov–Edel lengthening with (ri) = (7, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 16 times 0, 1, 22 times 0, 1, 27 times 0) [i] based on linear OA(4924, 78, F49, 22) (dual of [78, 54, 23]-code), using
(15, 37, 49537)-Net in Base 49 — Upper bound on s
There is no (15, 37, 49538)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 344 607948 643688 736878 605243 924816 381404 110162 831701 823488 321825 > 4937 [i]