Best Known (50−33, 50, s)-Nets in Base 49
(50−33, 50, 101)-Net over F49 — Constructive and digital
Digital (17, 50, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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, 34, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 16, 50)-net over F49, using
(50−33, 50, 114)-Net over F49 — Digital
Digital (17, 50, 114)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4950, 114, F49, 2, 33) (dual of [(114, 2), 178, 34]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(4916, 50, F49, 2, 16) (dual of [(50, 2), 84, 17]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;84,49) [i]
- linear OOA(4934, 64, F49, 2, 33) (dual of [(64, 2), 94, 34]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,94P) [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- linear OOA(4916, 50, F49, 2, 16) (dual of [(50, 2), 84, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
(50−33, 50, 21250)-Net in Base 49 — Upper bound on s
There is no (17, 50, 21251)-net in base 49, because
- 1 times m-reduction [i] would yield (17, 49, 21251)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 66049 697922 749864 451210 947464 560269 229983 593457 600112 545911 542377 860655 547872 467201 > 4949 [i]