Best Known (198, 198+44, s)-Nets in Base 2
(198, 198+44, 320)-Net over F2 — Constructive and digital
Digital (198, 242, 320)-net over F2, using
- 22 times duplication [i] based on digital (196, 240, 320)-net over F2, using
- t-expansion [i] based on digital (195, 240, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 48, 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
- trace code for nets [i] based on digital (3, 48, 64)-net over F32, using
- t-expansion [i] based on digital (195, 240, 320)-net over F2, using
(198, 198+44, 875)-Net over F2 — Digital
Digital (198, 242, 875)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2242, 875, F2, 2, 44) (dual of [(875, 2), 1508, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2242, 1024, F2, 2, 44) (dual of [(1024, 2), 1806, 45]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2242, 2048, F2, 44) (dual of [2048, 1806, 45]-code), using
- 1 times truncation [i] based on linear OA(2243, 2049, F2, 45) (dual of [2049, 1806, 46]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2243, 2049, F2, 45) (dual of [2049, 1806, 46]-code), using
- OOA 2-folding [i] based on linear OA(2242, 2048, F2, 44) (dual of [2048, 1806, 45]-code), using
- discarding factors / shortening the dual code based on linear OOA(2242, 1024, F2, 2, 44) (dual of [(1024, 2), 1806, 45]-NRT-code), using
(198, 198+44, 18510)-Net in Base 2 — Upper bound on s
There is no (198, 242, 18511)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 7 070296 305770 974361 255006 449274 742972 019834 473082 995203 189435 973063 283996 > 2242 [i]