Best Known (99, 120, s)-Nets in Base 4
(99, 120, 1653)-Net over F4 — Constructive and digital
Digital (99, 120, 1653)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (85, 106, 1638)-net over F4, using
- net defined by OOA [i] based on linear OOA(4106, 1638, F4, 21, 21) (dual of [(1638, 21), 34292, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4106, 16381, F4, 21) (dual of [16381, 16275, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4106, 16381, F4, 21) (dual of [16381, 16275, 22]-code), using
- net defined by OOA [i] based on linear OOA(4106, 1638, F4, 21, 21) (dual of [(1638, 21), 34292, 22]-NRT-code), using
- digital (4, 14, 15)-net over F4, using
(99, 120, 15577)-Net over F4 — Digital
Digital (99, 120, 15577)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4120, 15577, F4, 21) (dual of [15577, 15457, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4120, 16413, F4, 21) (dual of [16413, 16293, 22]-code), using
- (u, u+v)-construction [i] based on
- linear OA(414, 29, F4, 10) (dual of [29, 15, 11]-code), using
- 1 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,4) [i]
- 1 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(414, 29, F4, 10) (dual of [29, 15, 11]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4120, 16413, F4, 21) (dual of [16413, 16293, 22]-code), using
(99, 120, large)-Net in Base 4 — Upper bound on s
There is no (99, 120, large)-net in base 4, because
- 19 times m-reduction [i] would yield (99, 101, large)-net in base 4, but