Best Known (131, 158, s)-Nets in Base 4
(131, 158, 1542)-Net over F4 — Constructive and digital
Digital (131, 158, 1542)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (37, 50, 514)-net over F4, using
- trace code for nets [i] based on digital (12, 25, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(12,256) in PG(24,16)) for nets [i] based on digital (0, 13, 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
- base reduction for projective spaces (embedding PG(12,256) in PG(24,16)) for nets [i] based on digital (0, 13, 257)-net over F256, using
- trace code for nets [i] based on digital (12, 25, 257)-net over F16, using
- digital (81, 108, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 27, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 27, 257)-net over F256, using
- digital (37, 50, 514)-net over F4, using
(131, 158, 16447)-Net over F4 — Digital
Digital (131, 158, 16447)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4158, 16447, F4, 27) (dual of [16447, 16289, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(17) [i] based on
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(417, 63, F4, 8) (dual of [63, 46, 9]-code), using
- construction X applied to Ce(26) ⊂ Ce(17) [i] based on
(131, 158, large)-Net in Base 4 — Upper bound on s
There is no (131, 158, large)-net in base 4, because
- 25 times m-reduction [i] would yield (131, 133, large)-net in base 4, but