Best Known (162, 192, s)-Nets in Base 4
(162, 192, 4374)-Net over F4 — Constructive and digital
Digital (162, 192, 4374)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (147, 177, 4369)-net over F4, using
- net defined by OOA [i] based on linear OOA(4177, 4369, F4, 30, 30) (dual of [(4369, 30), 130893, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4177, 65535, F4, 30) (dual of [65535, 65358, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4177, 65535, F4, 30) (dual of [65535, 65358, 31]-code), using
- net defined by OOA [i] based on linear OOA(4177, 4369, F4, 30, 30) (dual of [(4369, 30), 130893, 31]-NRT-code), using
- digital (0, 15, 5)-net over F4, using
(162, 192, 48150)-Net over F4 — Digital
Digital (162, 192, 48150)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4192, 48150, F4, 30) (dual of [48150, 47958, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4192, 65552, F4, 30) (dual of [65552, 65360, 31]-code), using
- (u, u+v)-construction [i] based on
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4192, 65552, F4, 30) (dual of [65552, 65360, 31]-code), using
(162, 192, large)-Net in Base 4 — Upper bound on s
There is no (162, 192, large)-net in base 4, because
- 28 times m-reduction [i] would yield (162, 164, large)-net in base 4, but