Best Known (23−10, 23, s)-Nets in Base 5
(23−10, 23, 54)-Net over F5 — Constructive and digital
Digital (13, 23, 54)-net over F5, using
- 1 times m-reduction [i] based on digital (13, 24, 54)-net over F5, using
- trace code for nets [i] based on digital (1, 12, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- trace code for nets [i] based on digital (1, 12, 27)-net over F25, using
(23−10, 23, 75)-Net over F5 — Digital
Digital (13, 23, 75)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(523, 75, F5, 10) (dual of [75, 52, 11]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(522, 72, F5, 10) (dual of [72, 50, 11]-code), using
- trace code [i] based on linear OA(2511, 36, F25, 10) (dual of [36, 25, 11]-code), using
- extended algebraic-geometric code AGe(F,25P) [i] based on function field F/F25 with g(F) = 1 and N(F) ≥ 36, using
- trace code [i] based on linear OA(2511, 36, F25, 10) (dual of [36, 25, 11]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(522, 72, F5, 10) (dual of [72, 50, 11]-code), using
(23−10, 23, 1065)-Net in Base 5 — Upper bound on s
There is no (13, 23, 1066)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 11926 339798 381737 > 523 [i]