Best Known (216−21, 216, s)-Nets in Base 4
(216−21, 216, 839100)-Net over F4 — Constructive and digital
Digital (195, 216, 839100)-net over F4, using
- 42 times duplication [i] based on digital (193, 214, 839100)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (23, 33, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 11, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 11, 80)-net over F64, 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 (23, 33, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(216−21, 216, large)-Net over F4 — Digital
Digital (195, 216, large)-net over F4, using
- 1 times m-reduction [i] based on digital (195, 217, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
(216−21, 216, large)-Net in Base 4 — Upper bound on s
There is no (195, 216, large)-net in base 4, because
- 19 times m-reduction [i] would yield (195, 197, large)-net in base 4, but