Best Known (26, 26+29, s)-Nets in Base 5
(26, 26+29, 51)-Net over F5 — Constructive and digital
Digital (26, 55, 51)-net over F5, using
- t-expansion [i] based on digital (22, 55, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(26, 26+29, 56)-Net over F5 — Digital
Digital (26, 55, 56)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(555, 56, F5, 3, 29) (dual of [(56, 3), 113, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(552, 55, F5, 3, 29) (dual of [(55, 3), 113, 30]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,135P) [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(552, 55, F5, 3, 29) (dual of [(55, 3), 113, 30]-NRT-code), using
(26, 26+29, 740)-Net in Base 5 — Upper bound on s
There is no (26, 55, 741)-net in base 5, because
- 1 times m-reduction [i] would yield (26, 54, 741)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 55 846874 481028 909502 717139 463087 330665 > 554 [i]