Best Known (150, 150+33, s)-Nets in Base 4
(150, 150+33, 1539)-Net over F4 — Constructive and digital
Digital (150, 183, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 61, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(150, 150+33, 14152)-Net over F4 — Digital
Digital (150, 183, 14152)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 14152, F4, 33) (dual of [14152, 13969, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 16433, F4, 33) (dual of [16433, 16250, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4182, 16432, F4, 33) (dual of [16432, 16250, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 48, F4, 6) (dual of [48, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4182, 16432, F4, 33) (dual of [16432, 16250, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 16433, F4, 33) (dual of [16433, 16250, 34]-code), using
(150, 150+33, large)-Net in Base 4 — Upper bound on s
There is no (150, 183, large)-net in base 4, because
- 31 times m-reduction [i] would yield (150, 152, large)-net in base 4, but