Best Known (30, 47, s)-Nets in Base 8
(30, 47, 256)-Net over F8 — Constructive and digital
Digital (30, 47, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (30, 50, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 25, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 25, 128)-net over F64, using
(30, 47, 514)-Net in Base 8 — Constructive
(30, 47, 514)-net in base 8, using
- 1 times m-reduction [i] based on (30, 48, 514)-net in base 8, using
- base change [i] based on digital (18, 36, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 18, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 18, 257)-net over F256, using
- base change [i] based on digital (18, 36, 514)-net over F16, using
(30, 47, 529)-Net over F8 — Digital
Digital (30, 47, 529)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(847, 529, F8, 17) (dual of [529, 482, 18]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0) [i] based on linear OA(844, 516, F8, 17) (dual of [516, 472, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(843, 512, F8, 17) (dual of [512, 469, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(840, 512, F8, 15) (dual of [512, 472, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 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(16) ⊂ Ce(14) [i] based on
- 10 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0) [i] based on linear OA(844, 516, F8, 17) (dual of [516, 472, 18]-code), using
(30, 47, 83817)-Net in Base 8 — Upper bound on s
There is no (30, 47, 83818)-net in base 8, because
- 1 times m-reduction [i] would yield (30, 46, 83818)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 348461 330351 106481 710980 903634 709341 831949 > 846 [i]