Best Known (141−15, 141, s)-Nets in Base 4
(141−15, 141, 1198380)-Net over F4 — Constructive and digital
Digital (126, 141, 1198380)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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 (118, 133, 1198371)-net over F4, using
- net defined by OOA [i] based on linear OOA(4133, 1198371, F4, 15, 15) (dual of [(1198371, 15), 17975432, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4133, 8388598, F4, 15) (dual of [8388598, 8388465, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4133, large, F4, 15) (dual of [large, large−133, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(4133, large, F4, 15) (dual of [large, large−133, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4133, 8388598, F4, 15) (dual of [8388598, 8388465, 16]-code), using
- net defined by OOA [i] based on linear OOA(4133, 1198371, F4, 15, 15) (dual of [(1198371, 15), 17975432, 16]-NRT-code), using
- digital (1, 8, 9)-net over F4, using
(141−15, 141, 5754494)-Net over F4 — Digital
Digital (126, 141, 5754494)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4141, 5754494, F4, 15) (dual of [5754494, 5754353, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, large, F4, 15) (dual of [large, large−141, 16]-code), using
- 8 times code embedding in larger space [i] based on linear OA(4133, large, F4, 15) (dual of [large, large−133, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 8 times code embedding in larger space [i] based on linear OA(4133, large, F4, 15) (dual of [large, large−133, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, large, F4, 15) (dual of [large, large−141, 16]-code), using
(141−15, 141, large)-Net in Base 4 — Upper bound on s
There is no (126, 141, large)-net in base 4, because
- 13 times m-reduction [i] would yield (126, 128, large)-net in base 4, but