Best Known (203, 203+33, s)-Nets in Base 4
(203, 203+33, 16398)-Net over F4 — Constructive and digital
Digital (203, 236, 16398)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 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 (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 (3, 19, 14)-net over F4, using
(203, 203+33, 151650)-Net over F4 — Digital
Digital (203, 236, 151650)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 151650, F4, 33) (dual of [151650, 151414, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 262218, F4, 33) (dual of [262218, 261982, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4234, 262216, F4, 33) (dual of [262216, 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(417, 71, F4, 7) (dual of [71, 54, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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 Ce(6) ⊂ Ce(4) [i] based on
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4234, 262216, F4, 33) (dual of [262216, 261982, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 262218, F4, 33) (dual of [262218, 261982, 34]-code), using
(203, 203+33, large)-Net in Base 4 — Upper bound on s
There is no (203, 236, large)-net in base 4, because
- 31 times m-reduction [i] would yield (203, 205, large)-net in base 4, but