Best Known (183, 183+22, s)-Nets in Base 4
(183, 183+22, 762609)-Net over F4 — Constructive and digital
Digital (183, 205, 762609)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (171, 193, 762600)-net over F4, using
- net defined by OOA [i] based on linear OOA(4193, 762600, F4, 22, 22) (dual of [(762600, 22), 16777007, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4193, 8388600, F4, 22) (dual of [8388600, 8388407, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4193, 8388600, F4, 22) (dual of [8388600, 8388407, 23]-code), using
- net defined by OOA [i] based on linear OOA(4193, 762600, F4, 22, 22) (dual of [(762600, 22), 16777007, 23]-NRT-code), using
- digital (1, 12, 9)-net over F4, using
(183, 183+22, 4194310)-Net over F4 — Digital
Digital (183, 205, 4194310)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4205, 4194310, F4, 2, 22) (dual of [(4194310, 2), 8388415, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(412, 9, F4, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,6P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- extended algebraic-geometric NRT-code AGe(2;F,6P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- linear OOA(4193, 4194301, F4, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- linear OOA(412, 9, F4, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(183, 183+22, large)-Net in Base 4 — Upper bound on s
There is no (183, 205, large)-net in base 4, because
- 20 times m-reduction [i] would yield (183, 185, large)-net in base 4, but