Best Known (29−16, 29, s)-Nets in Base 49
(29−16, 29, 150)-Net over F49 — Constructive and digital
Digital (13, 29, 150)-net over F49, using
- 1 times m-reduction [i] based on digital (13, 30, 150)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 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 (0, 8, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 17, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 5, 50)-net over F49, using
- generalized (u, u+v)-construction [i] based on
(29−16, 29, 297)-Net over F49 — Digital
Digital (13, 29, 297)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4929, 297, F49, 16) (dual of [297, 268, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 300, F49, 16) (dual of [300, 271, 17]-code), using
(29−16, 29, 105049)-Net in Base 49 — Upper bound on s
There is no (13, 29, 105050)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 10 368098 043206 924914 124103 330988 941559 131130 202881 > 4929 [i]