Best Known (10, 28, s)-Nets in Base 49
(10, 28, 101)-Net over F49 — Constructive and digital
Digital (10, 28, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (1, 19, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 9, 50)-net over F49, using
(10, 28, 114)-Net over F49 — Digital
Digital (10, 28, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4928, 114, F49, 3, 18) (dual of [(114, 3), 314, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(499, 50, F49, 3, 9) (dual of [(50, 3), 141, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;141,49) [i]
- linear OOA(4919, 64, F49, 3, 18) (dual of [(64, 3), 173, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,173P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(499, 50, F49, 3, 9) (dual of [(50, 3), 141, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(10, 28, 15659)-Net in Base 49 — Upper bound on s
There is no (10, 28, 15660)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 211630 810445 323898 559230 860101 388130 808916 685377 > 4928 [i]