Best Known (46, 78, s)-Nets in Base 9
(46, 78, 344)-Net over F9 — Constructive and digital
Digital (46, 78, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 39, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(46, 78, 408)-Net over F9 — Digital
Digital (46, 78, 408)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(978, 408, F9, 32) (dual of [408, 330, 33]-code), using
- 26 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0, 1, 18 times 0) [i] based on linear OA(976, 380, F9, 32) (dual of [380, 304, 33]-code), using
- trace code [i] based on linear OA(8138, 190, F81, 32) (dual of [190, 152, 33]-code), using
- extended algebraic-geometric code AGe(F,157P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8138, 190, F81, 32) (dual of [190, 152, 33]-code), using
- 26 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0, 1, 18 times 0) [i] based on linear OA(976, 380, F9, 32) (dual of [380, 304, 33]-code), using
(46, 78, 38130)-Net in Base 9 — Upper bound on s
There is no (46, 78, 38131)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 269 775297 608101 068752 152275 579309 103977 153158 185436 176275 246027 697772 076417 > 978 [i]