Best Known (203, 203+34, s)-Nets in Base 2
(203, 203+34, 768)-Net over F2 — Constructive and digital
Digital (203, 237, 768)-net over F2, using
- 23 times duplication [i] based on digital (200, 234, 768)-net over F2, using
- trace code for nets [i] based on digital (5, 39, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 39, 128)-net over F64, using
(203, 203+34, 2641)-Net over F2 — Digital
Digital (203, 237, 2641)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2237, 2641, F2, 3, 34) (dual of [(2641, 3), 7686, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2237, 2748, F2, 3, 34) (dual of [(2748, 3), 8007, 35]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2235, 2748, F2, 3, 34) (dual of [(2748, 3), 8009, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2235, 8244, F2, 34) (dual of [8244, 8009, 35]-code), using
- strength reduction [i] based on linear OA(2235, 8244, F2, 35) (dual of [8244, 8009, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(213, 52, F2, 5) (dual of [52, 39, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- strength reduction [i] based on linear OA(2235, 8244, F2, 35) (dual of [8244, 8009, 36]-code), using
- OOA 3-folding [i] based on linear OA(2235, 8244, F2, 34) (dual of [8244, 8009, 35]-code), using
- 22 times duplication [i] based on linear OOA(2235, 2748, F2, 3, 34) (dual of [(2748, 3), 8009, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2237, 2748, F2, 3, 34) (dual of [(2748, 3), 8007, 35]-NRT-code), using
(203, 203+34, 112865)-Net in Base 2 — Upper bound on s
There is no (203, 237, 112866)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 220871 541256 152417 553285 461949 298288 906085 245925 435693 738621 523929 005902 > 2237 [i]