Best Known (10, 27, s)-Nets in Base 49
(10, 27, 102)-Net over F49 — Constructive and digital
Digital (10, 27, 102)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 18, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- digital (1, 9, 51)-net over F49, using
(10, 27, 128)-Net over F49 — Digital
Digital (10, 27, 128)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4927, 128, F49, 3, 17) (dual of [(128, 3), 357, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(499, 64, F49, 3, 8) (dual of [(64, 3), 183, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,183P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(4918, 64, F49, 3, 17) (dual of [(64, 3), 174, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,174P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64 (see above)
- linear OOA(499, 64, F49, 3, 8) (dual of [(64, 3), 183, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(10, 27, 24407)-Net in Base 49 — Upper bound on s
There is no (10, 27, 24408)-net in base 49, because
- 1 times m-reduction [i] would yield (10, 26, 24408)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 88 143198 552520 565329 433477 864925 644556 063745 > 4926 [i]