Best Known (181, 210, s)-Nets in Base 4
(181, 210, 18742)-Net over F4 — Constructive and digital
Digital (181, 210, 18742)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (162, 191, 18725)-net over F4, using
- net defined by OOA [i] based on linear OOA(4191, 18725, F4, 29, 29) (dual of [(18725, 29), 542834, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4191, 262151, F4, 29) (dual of [262151, 261960, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4191, 262154, F4, 29) (dual of [262154, 261963, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4181, 262144, F4, 27) (dual of [262144, 261963, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(41, 10, F4, 1) (dual of [10, 9, 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
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4191, 262154, F4, 29) (dual of [262154, 261963, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4191, 262151, F4, 29) (dual of [262151, 261960, 30]-code), using
- net defined by OOA [i] based on linear OOA(4191, 18725, F4, 29, 29) (dual of [(18725, 29), 542834, 30]-NRT-code), using
- digital (5, 19, 17)-net over F4, using
(181, 210, 166579)-Net over F4 — Digital
Digital (181, 210, 166579)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4210, 166579, F4, 29) (dual of [166579, 166369, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4210, 262170, F4, 29) (dual of [262170, 261960, 30]-code), using
- (u, u+v)-construction [i] based on
- linear OA(420, 26, F4, 14) (dual of [26, 6, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(420, 27, F4, 14) (dual of [27, 7, 15]-code), using
- 1 times truncation [i] based on linear OA(421, 28, F4, 15) (dual of [28, 7, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(420, 27, F4, 14) (dual of [27, 7, 15]-code), using
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(420, 26, F4, 14) (dual of [26, 6, 15]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4210, 262170, F4, 29) (dual of [262170, 261960, 30]-code), using
(181, 210, large)-Net in Base 4 — Upper bound on s
There is no (181, 210, large)-net in base 4, because
- 27 times m-reduction [i] would yield (181, 183, large)-net in base 4, but