Best Known (202, 202+35, s)-Nets in Base 4
(202, 202+35, 15421)-Net over F4 — Constructive and digital
Digital (202, 237, 15421)-net over F4, using
- 41 times duplication [i] based on digital (201, 236, 15421)-net over F4, using
- net defined by OOA [i] based on linear OOA(4236, 15421, F4, 35, 35) (dual of [(15421, 35), 539499, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(4236, 262158, F4, 35) (dual of [262158, 261922, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 262164, F4, 35) (dual of [262164, 261928, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,16]) [i] based on
- linear OA(4235, 262145, F4, 35) (dual of [262145, 261910, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- 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(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([0,17]) ⊂ C([0,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4236, 262164, F4, 35) (dual of [262164, 261928, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(4236, 262158, F4, 35) (dual of [262158, 261922, 36]-code), using
- net defined by OOA [i] based on linear OOA(4236, 15421, F4, 35, 35) (dual of [(15421, 35), 539499, 36]-NRT-code), using
(202, 202+35, 112470)-Net over F4 — Digital
Digital (202, 237, 112470)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4237, 112470, F4, 2, 35) (dual of [(112470, 2), 224703, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4237, 131082, F4, 2, 35) (dual of [(131082, 2), 261927, 36]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4236, 131082, F4, 2, 35) (dual of [(131082, 2), 261928, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4236, 262164, F4, 35) (dual of [262164, 261928, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,16]) [i] based on
- linear OA(4235, 262145, F4, 35) (dual of [262145, 261910, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- 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(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([0,17]) ⊂ C([0,16]) [i] based on
- OOA 2-folding [i] based on linear OA(4236, 262164, F4, 35) (dual of [262164, 261928, 36]-code), using
- 41 times duplication [i] based on linear OOA(4236, 131082, F4, 2, 35) (dual of [(131082, 2), 261928, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4237, 131082, F4, 2, 35) (dual of [(131082, 2), 261927, 36]-NRT-code), using
(202, 202+35, large)-Net in Base 4 — Upper bound on s
There is no (202, 237, large)-net in base 4, because
- 33 times m-reduction [i] would yield (202, 204, large)-net in base 4, but