Best Known (200, 243, s)-Nets in Base 2
(200, 243, 380)-Net over F2 — Constructive and digital
Digital (200, 243, 380)-net over F2, using
- 23 times duplication [i] based on digital (197, 240, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 48, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- trace code for nets [i] based on digital (5, 48, 76)-net over F32, using
(200, 243, 970)-Net over F2 — Digital
Digital (200, 243, 970)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2243, 970, F2, 2, 43) (dual of [(970, 2), 1697, 44]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2243, 1042, F2, 2, 43) (dual of [(1042, 2), 1841, 44]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2243, 2084, F2, 43) (dual of [2084, 1841, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(2243, 2085, F2, 43) (dual of [2085, 1842, 44]-code), using
- construction XX applied to Ce(42) ⊂ Ce(38) ⊂ Ce(36) [i] based on
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction XX applied to Ce(42) ⊂ Ce(38) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(2243, 2085, F2, 43) (dual of [2085, 1842, 44]-code), using
- OOA 2-folding [i] based on linear OA(2243, 2084, F2, 43) (dual of [2084, 1841, 44]-code), using
- discarding factors / shortening the dual code based on linear OOA(2243, 1042, F2, 2, 43) (dual of [(1042, 2), 1841, 44]-NRT-code), using
(200, 243, 25525)-Net in Base 2 — Upper bound on s
There is no (200, 243, 25526)-net in base 2, because
- 1 times m-reduction [i] would yield (200, 242, 25526)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7 068988 977222 346101 339405 019292 287720 524176 083211 918002 904509 419198 825997 > 2242 [i]