Best Known (11, 11+18, s)-Nets in Base 49
(11, 11+18, 102)-Net over F49 — Constructive and digital
Digital (11, 29, 102)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 19, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- digital (1, 10, 51)-net over F49, using
(11, 11+18, 128)-Net over F49 — Digital
Digital (11, 29, 128)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4929, 128, F49, 2, 18) (dual of [(128, 2), 227, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(4910, 64, F49, 2, 9) (dual of [(64, 2), 118, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,118P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(4919, 64, F49, 2, 18) (dual of [(64, 2), 109, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,109P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64 (see above)
- linear OOA(4910, 64, F49, 2, 9) (dual of [(64, 2), 118, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(11, 11+18, 24133)-Net in Base 49 — Upper bound on s
There is no (11, 29, 24134)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 10 369313 006769 607331 483739 649988 931085 560277 772833 > 4929 [i]