Best Known (39−15, 39, s)-Nets in Base 8
(39−15, 39, 208)-Net over F8 — Constructive and digital
Digital (24, 39, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (24, 42, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 21, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 21, 104)-net over F64, using
(39−15, 39, 291)-Net over F8 — Digital
Digital (24, 39, 291)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(839, 291, F8, 15) (dual of [291, 252, 16]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 20 times 0, 1, 34 times 0) [i] based on linear OA(836, 226, F8, 15) (dual of [226, 190, 16]-code), using
- trace code [i] based on linear OA(6418, 113, F64, 15) (dual of [113, 95, 16]-code), using
- extended algebraic-geometric code AGe(F,97P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- trace code [i] based on linear OA(6418, 113, F64, 15) (dual of [113, 95, 16]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 20 times 0, 1, 34 times 0) [i] based on linear OA(836, 226, F8, 15) (dual of [226, 190, 16]-code), using
(39−15, 39, 300)-Net in Base 8 — Constructive
(24, 39, 300)-net in base 8, using
- 1 times m-reduction [i] based on (24, 40, 300)-net in base 8, using
- trace code for nets [i] based on (4, 20, 150)-net in base 64, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- trace code for nets [i] based on (4, 20, 150)-net in base 64, using
(39−15, 39, 38571)-Net in Base 8 — Upper bound on s
There is no (24, 39, 38572)-net in base 8, because
- 1 times m-reduction [i] would yield (24, 38, 38572)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 20771 893334 973214 535592 563450 523566 > 838 [i]