Best Known (196−21, 196, s)-Nets in Base 4
(196−21, 196, 838877)-Net over F4 — Constructive and digital
Digital (175, 196, 838877)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 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 (160, 181, 838860)-net over F4, using
- net defined by OOA [i] based on linear OOA(4181, 838860, F4, 21, 21) (dual of [(838860, 21), 17615879, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4181, 8388601, F4, 21) (dual of [8388601, 8388420, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4181, 8388601, F4, 21) (dual of [8388601, 8388420, 22]-code), using
- net defined by OOA [i] based on linear OOA(4181, 838860, F4, 21, 21) (dual of [(838860, 21), 17615879, 22]-NRT-code), using
- digital (5, 15, 17)-net over F4, using
(196−21, 196, 4194318)-Net over F4 — Digital
Digital (175, 196, 4194318)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4196, 4194318, F4, 2, 21) (dual of [(4194318, 2), 8388440, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(415, 17, F4, 2, 10) (dual of [(17, 2), 19, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,23P) [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- linear OOA(4181, 4194301, F4, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- linear OOA(415, 17, F4, 2, 10) (dual of [(17, 2), 19, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(196−21, 196, large)-Net in Base 4 — Upper bound on s
There is no (175, 196, large)-net in base 4, because
- 19 times m-reduction [i] would yield (175, 177, large)-net in base 4, but