Best Known (201, 246, s)-Nets in Base 4
(201, 246, 1556)-Net over F4 — Constructive and digital
Digital (201, 246, 1556)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 27, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (174, 219, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 73, 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
- trace code for nets [i] based on digital (28, 73, 513)-net over F64, using
- digital (5, 27, 17)-net over F4, using
(201, 246, 15125)-Net over F4 — Digital
Digital (201, 246, 15125)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4246, 15125, F4, 45) (dual of [15125, 14879, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 16433, F4, 45) (dual of [16433, 16187, 46]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4245, 16432, F4, 45) (dual of [16432, 16187, 46]-code), using
- construction X applied to Ce(44) ⊂ Ce(37) [i] based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(44) ⊂ Ce(37) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4245, 16432, F4, 45) (dual of [16432, 16187, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 16433, F4, 45) (dual of [16433, 16187, 46]-code), using
(201, 246, large)-Net in Base 4 — Upper bound on s
There is no (201, 246, large)-net in base 4, because
- 43 times m-reduction [i] would yield (201, 203, large)-net in base 4, but