Best Known (202, 202+47, s)-Nets in Base 4
(202, 202+47, 1548)-Net over F4 — Constructive and digital
Digital (202, 249, 1548)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 24, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (178, 225, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 75, 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, 75, 513)-net over F64, using
- digital (1, 24, 9)-net over F4, using
(202, 202+47, 12184)-Net over F4 — Digital
Digital (202, 249, 12184)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4249, 12184, F4, 47) (dual of [12184, 11935, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(4249, 16402, F4, 47) (dual of [16402, 16153, 48]-code), using
- construction XX applied to Ce(46) ⊂ Ce(44) ⊂ Ce(42) [i] based on
- linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- 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(4225, 16384, F4, 43) (dual of [16384, 16159, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(46) ⊂ Ce(44) ⊂ Ce(42) [i] based on
- discarding factors / shortening the dual code based on linear OA(4249, 16402, F4, 47) (dual of [16402, 16153, 48]-code), using
(202, 202+47, large)-Net in Base 4 — Upper bound on s
There is no (202, 249, large)-net in base 4, because
- 45 times m-reduction [i] would yield (202, 204, large)-net in base 4, but