Best Known (218−34, 218, s)-Nets in Base 4
(218−34, 218, 3860)-Net over F4 — Constructive and digital
Digital (184, 218, 3860)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 17, 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 (167, 201, 3855)-net over F4, using
- net defined by OOA [i] based on linear OOA(4201, 3855, F4, 34, 34) (dual of [(3855, 34), 130869, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(4201, 65535, F4, 34) (dual of [65535, 65334, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(4201, 65535, F4, 34) (dual of [65535, 65334, 35]-code), using
- net defined by OOA [i] based on linear OOA(4201, 3855, F4, 34, 34) (dual of [(3855, 34), 130869, 35]-NRT-code), using
- digital (0, 17, 5)-net over F4, using
(218−34, 218, 51554)-Net over F4 — Digital
Digital (184, 218, 51554)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4218, 51554, F4, 34) (dual of [51554, 51336, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4218, 65554, F4, 34) (dual of [65554, 65336, 35]-code), using
- (u, u+v)-construction [i] based on
- linear OA(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
- dual of repetition code with length 18 [i]
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4218, 65554, F4, 34) (dual of [65554, 65336, 35]-code), using
(218−34, 218, large)-Net in Base 4 — Upper bound on s
There is no (184, 218, large)-net in base 4, because
- 32 times m-reduction [i] would yield (184, 186, large)-net in base 4, but