Best Known (130−23, 130, s)-Nets in Base 2
(130−23, 130, 320)-Net over F2 — Constructive and digital
Digital (107, 130, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 26, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
(130−23, 130, 692)-Net over F2 — Digital
Digital (107, 130, 692)-net over F2, using
- 22 times duplication [i] based on digital (105, 128, 692)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2128, 692, F2, 3, 23) (dual of [(692, 3), 1948, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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(22) ⊂ Ce(18) [i] based on
- OOA 3-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2128, 692, F2, 3, 23) (dual of [(692, 3), 1948, 24]-NRT-code), using
(130−23, 130, 16628)-Net in Base 2 — Upper bound on s
There is no (107, 130, 16629)-net in base 2, because
- 1 times m-reduction [i] would yield (107, 129, 16629)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 680 713078 060784 945038 699907 747640 770560 > 2129 [i]