Best Known (193, 193+42, s)-Nets in Base 4
(193, 193+42, 1554)-Net over F4 — Constructive and digital
Digital (193, 235, 1554)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (168, 210, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 70, 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, 70, 513)-net over F64, using
- digital (4, 25, 15)-net over F4, using
(193, 193+42, 16447)-Net over F4 — Digital
Digital (193, 235, 16447)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4235, 16447, F4, 42) (dual of [16447, 16212, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(32) [i] based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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(417, 63, F4, 8) (dual of [63, 46, 9]-code), using
- construction X applied to Ce(41) ⊂ Ce(32) [i] based on
(193, 193+42, large)-Net in Base 4 — Upper bound on s
There is no (193, 235, large)-net in base 4, because
- 40 times m-reduction [i] would yield (193, 195, large)-net in base 4, but