Best Known (202, 202+33, s)-Nets in Base 4
(202, 202+33, 16394)-Net over F4 — Constructive and digital
Digital (202, 235, 16394)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 18, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (184, 217, 16384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- digital (2, 18, 10)-net over F4, using
(202, 202+33, 145017)-Net over F4 — Digital
Digital (202, 235, 145017)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4235, 145017, F4, 33) (dual of [145017, 144782, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4235, 262217, F4, 33) (dual of [262217, 261982, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(418, 72, F4, 7) (dual of [72, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4235, 262217, F4, 33) (dual of [262217, 261982, 34]-code), using
(202, 202+33, large)-Net in Base 4 — Upper bound on s
There is no (202, 235, large)-net in base 4, because
- 31 times m-reduction [i] would yield (202, 204, large)-net in base 4, but