Best Known (183, 215, s)-Nets in Base 4
(183, 215, 4117)-Net over F4 — Constructive and digital
Digital (183, 215, 4117)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (160, 192, 4096)-net over F4, using
- net defined by OOA [i] based on linear OOA(4192, 4096, F4, 32, 32) (dual of [(4096, 32), 130880, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(4192, 65536, F4, 32) (dual of [65536, 65344, 33]-code), using
- 1 times truncation [i] based on linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(4192, 65536, F4, 32) (dual of [65536, 65344, 33]-code), using
- net defined by OOA [i] based on linear OOA(4192, 4096, F4, 32, 32) (dual of [(4096, 32), 130880, 33]-NRT-code), using
- digital (7, 23, 21)-net over F4, using
(183, 215, 65623)-Net over F4 — Digital
Digital (183, 215, 65623)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4215, 65623, F4, 32) (dual of [65623, 65408, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4214, 65621, F4, 32) (dual of [65621, 65407, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(21) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(32) ⊂ Ce(21) [i] based on
- linear OA(4214, 65622, F4, 31) (dual of [65622, 65408, 32]-code), using Gilbert–Varšamov bound and bm = 4214 > Vbs−1(k−1) = 2 502936 050615 400529 190553 521166 057942 047489 632173 226640 437710 854803 543500 502033 266486 166211 686806 997824 652970 105706 716830 186336 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(4214, 65621, F4, 32) (dual of [65621, 65407, 33]-code), using
- construction X with Varšamov bound [i] based on
(183, 215, large)-Net in Base 4 — Upper bound on s
There is no (183, 215, large)-net in base 4, because
- 30 times m-reduction [i] would yield (183, 185, large)-net in base 4, but