Best Known (29−16, 29, s)-Nets in Base 64
(29−16, 29, 195)-Net over F64 — Constructive and digital
Digital (13, 29, 195)-net over F64, using
- 1 times m-reduction [i] based on digital (13, 30, 195)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (0, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 17, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 5, 65)-net over F64, using
- generalized (u, u+v)-construction [i] based on
(29−16, 29, 262)-Net in Base 64 — Constructive
(13, 29, 262)-net in base 64, using
- 3 times m-reduction [i] based on (13, 32, 262)-net in base 64, using
- base change [i] based on digital (5, 24, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- base change [i] based on digital (5, 24, 262)-net over F256, using
(29−16, 29, 387)-Net over F64 — Digital
Digital (13, 29, 387)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6429, 387, F64, 16) (dual of [387, 358, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, 455, F64, 16) (dual of [455, 426, 17]-code), using
(29−16, 29, 210738)-Net in Base 64 — Upper bound on s
There is no (13, 29, 210739)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 23945 449119 632735 159978 754530 200716 605015 906428 274650 > 6429 [i]