Best Known (179−31, 179, s)-Nets in Base 4
(179−31, 179, 1539)-Net over F4 — Constructive and digital
Digital (148, 179, 1539)-net over F4, using
- 1 times m-reduction [i] based on digital (148, 180, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 60, 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, 60, 513)-net over F64, using
(179−31, 179, 16447)-Net over F4 — Digital
Digital (148, 179, 16447)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4179, 16447, F4, 31) (dual of [16447, 16268, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(417, 63, F4, 8) (dual of [63, 46, 9]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
(179−31, 179, large)-Net in Base 4 — Upper bound on s
There is no (148, 179, large)-net in base 4, because
- 29 times m-reduction [i] would yield (148, 150, large)-net in base 4, but