Best Known (46, 46+28, s)-Nets in Base 8
(46, 46+28, 354)-Net over F8 — Constructive and digital
Digital (46, 74, 354)-net over F8, using
- 4 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, 46+28, 384)-Net in Base 8 — Constructive
(46, 74, 384)-net in base 8, using
- trace code for nets [i] based on (9, 37, 192)-net in base 64, using
- 5 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- 5 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
(46, 46+28, 503)-Net over F8 — Digital
Digital (46, 74, 503)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(874, 503, F8, 28) (dual of [503, 429, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(874, 519, F8, 28) (dual of [519, 445, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(873, 512, F8, 28) (dual of [512, 439, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(874, 519, F8, 28) (dual of [519, 445, 29]-code), using
(46, 46+28, 51258)-Net in Base 8 — Upper bound on s
There is no (46, 74, 51259)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6 741462 394323 631753 730645 708893 507582 988413 534705 291874 915310 188508 > 874 [i]