Best Known (46, 72, s)-Nets in Base 8
(46, 72, 354)-Net over F8 — Constructive and digital
Digital (46, 72, 354)-net over F8, using
- 6 times m-reduction [i] based on digital (46, 78, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 39, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 39, 177)-net over F64, using
(46, 72, 516)-Net in Base 8 — Constructive
(46, 72, 516)-net in base 8, using
- base change [i] based on digital (28, 54, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 27, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 27, 258)-net over F256, using
(46, 72, 595)-Net over F8 — Digital
Digital (46, 72, 595)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(872, 595, F8, 26) (dual of [595, 523, 27]-code), using
- 75 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 22 times 0, 1, 36 times 0) [i] based on linear OA(867, 515, F8, 26) (dual of [515, 448, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(867, 512, F8, 26) (dual of [512, 445, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(864, 512, F8, 25) (dual of [512, 448, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 75 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 22 times 0, 1, 36 times 0) [i] based on linear OA(867, 515, F8, 26) (dual of [515, 448, 27]-code), using
(46, 72, 81282)-Net in Base 8 — Upper bound on s
There is no (46, 72, 81283)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 105326 177704 736165 933193 559609 023486 261982 504461 936048 576691 772736 > 872 [i]