Best Known (193−20, 193, s)-Nets in Base 4
(193−20, 193, 838874)-Net over F4 — Constructive and digital
Digital (173, 193, 838874)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (160, 180, 838860)-net over F4, using
- net defined by OOA [i] based on linear OOA(4180, 838860, F4, 20, 20) (dual of [(838860, 20), 16777020, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4180, 8388600, F4, 20) (dual of [8388600, 8388420, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4180, 8388600, F4, 20) (dual of [8388600, 8388420, 21]-code), using
- net defined by OOA [i] based on linear OOA(4180, 838860, F4, 20, 20) (dual of [(838860, 20), 16777020, 21]-NRT-code), using
- digital (3, 13, 14)-net over F4, using
(193−20, 193, 6652442)-Net over F4 — Digital
Digital (173, 193, 6652442)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4193, 6652442, F4, 20) (dual of [6652442, 6652249, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 20) (dual of [large, large−193, 21]-code), using
- strength reduction [i] 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]
- strength reduction [i] based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 20) (dual of [large, large−193, 21]-code), using
(193−20, 193, large)-Net in Base 4 — Upper bound on s
There is no (173, 193, large)-net in base 4, because
- 18 times m-reduction [i] would yield (173, 175, large)-net in base 4, but