Best Known (173, 200, s)-Nets in Base 4
(173, 200, 20183)-Net over F4 — Constructive and digital
Digital (173, 200, 20183)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 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 (155, 182, 20166)-net over F4, using
- net defined by OOA [i] based on linear OOA(4182, 20166, F4, 27, 27) (dual of [(20166, 27), 544300, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4182, 262159, F4, 27) (dual of [262159, 261977, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 262164, F4, 27) (dual of [262164, 261982, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(41, 19, F4, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4182, 262164, F4, 27) (dual of [262164, 261982, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4182, 262159, F4, 27) (dual of [262159, 261977, 28]-code), using
- net defined by OOA [i] based on linear OOA(4182, 20166, F4, 27, 27) (dual of [(20166, 27), 544300, 28]-NRT-code), using
- digital (5, 18, 17)-net over F4, using
(173, 200, 210311)-Net over F4 — Digital
Digital (173, 200, 210311)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4200, 210311, F4, 27) (dual of [210311, 210111, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, 262170, F4, 27) (dual of [262170, 261970, 28]-code), using
- (u, u+v)-construction [i] based on
- linear OA(419, 25, F4, 13) (dual of [25, 6, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 26, F4, 13) (dual of [26, 7, 14]-code), using
- 2 times truncation [i] based on linear OA(421, 28, F4, 15) (dual of [28, 7, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 26, F4, 13) (dual of [26, 7, 14]-code), using
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(419, 25, F4, 13) (dual of [25, 6, 14]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4200, 262170, F4, 27) (dual of [262170, 261970, 28]-code), using
(173, 200, large)-Net in Base 4 — Upper bound on s
There is no (173, 200, large)-net in base 4, because
- 25 times m-reduction [i] would yield (173, 175, large)-net in base 4, but