Best Known (41−16, 41, s)-Nets in Base 8
(41−16, 41, 208)-Net over F8 — Constructive and digital
Digital (25, 41, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (25, 44, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 22, 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, 22, 104)-net over F64, using
(41−16, 41, 281)-Net over F8 — Digital
Digital (25, 41, 281)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(841, 281, F8, 16) (dual of [281, 240, 17]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(840, 258, F8, 16) (dual of [258, 218, 17]-code), using
- trace code [i] based on linear OA(6420, 129, F64, 16) (dual of [129, 109, 17]-code), using
- extended algebraic-geometric code AGe(F,112P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6420, 129, F64, 16) (dual of [129, 109, 17]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(840, 258, F8, 16) (dual of [258, 218, 17]-code), using
(41−16, 41, 300)-Net in Base 8 — Constructive
(25, 41, 300)-net in base 8, using
- 1 times m-reduction [i] based on (25, 42, 300)-net in base 8, using
- trace code for nets [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
- trace code for nets [i] based on (4, 21, 150)-net in base 64, using
(41−16, 41, 22847)-Net in Base 8 — Upper bound on s
There is no (25, 41, 22848)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 10 635433 802567 337401 059672 940722 501001 > 841 [i]