Best Known (238−38, 238, s)-Nets in Base 2
(238−38, 238, 520)-Net over F2 — Constructive and digital
Digital (200, 238, 520)-net over F2, using
- 23 times duplication [i] based on digital (197, 235, 520)-net over F2, using
- trace code for nets [i] based on digital (9, 47, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- trace code for nets [i] based on digital (9, 47, 104)-net over F32, using
(238−38, 238, 1439)-Net over F2 — Digital
Digital (200, 238, 1439)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2238, 1439, F2, 2, 38) (dual of [(1439, 2), 2640, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2238, 2064, F2, 2, 38) (dual of [(2064, 2), 3890, 39]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2237, 2064, F2, 2, 38) (dual of [(2064, 2), 3891, 39]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2235, 2063, F2, 2, 38) (dual of [(2063, 2), 3891, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2235, 4126, F2, 38) (dual of [4126, 3891, 39]-code), using
- strength reduction [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- strength reduction [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-code), using
- OOA 2-folding [i] based on linear OA(2235, 4126, F2, 38) (dual of [4126, 3891, 39]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2235, 2063, F2, 2, 38) (dual of [(2063, 2), 3891, 39]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2237, 2064, F2, 2, 38) (dual of [(2064, 2), 3891, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2238, 2064, F2, 2, 38) (dual of [(2064, 2), 3890, 39]-NRT-code), using
(238−38, 238, 46746)-Net in Base 2 — Upper bound on s
There is no (200, 238, 46747)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 441739 423554 132182 564722 374820 939517 737842 560342 590056 058884 036249 008938 > 2238 [i]