Best Known (11, 11+15, s)-Nets in Base 49
(11, 11+15, 104)-Net over F49 — Constructive and digital
Digital (11, 26, 104)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (2, 17, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49 (see above)
- digital (2, 9, 52)-net over F49, using
(11, 11+15, 181)-Net over F49 — Digital
Digital (11, 26, 181)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4926, 181, F49, 15) (dual of [181, 155, 16]-code), using
- 107 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 29 times 0, 1, 40 times 0) [i] based on linear OA(4916, 64, F49, 15) (dual of [64, 48, 16]-code), using
- extended algebraic-geometric code AGe(F,48P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- 107 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 29 times 0, 1, 40 times 0) [i] based on linear OA(4916, 64, F49, 15) (dual of [64, 48, 16]-code), using
(11, 11+15, 76572)-Net in Base 49 — Upper bound on s
There is no (11, 26, 76573)-net in base 49, because
- 1 times m-reduction [i] would yield (11, 25, 76573)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 1 798509 151497 151664 766782 246346 492269 440273 > 4925 [i]