Best Known (199, 243, s)-Nets in Base 3
(199, 243, 1480)-Net over F3 — Constructive and digital
Digital (199, 243, 1480)-net over F3, using
- 1 times m-reduction [i] based on digital (199, 244, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 61, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 61, 370)-net over F81, using
(199, 243, 4593)-Net over F3 — Digital
Digital (199, 243, 4593)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3243, 4593, F3, 44) (dual of [4593, 4350, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3243, 6597, F3, 44) (dual of [6597, 6354, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(37) [i] based on
- linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- construction X applied to Ce(43) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(3243, 6597, F3, 44) (dual of [6597, 6354, 45]-code), using
(199, 243, 843010)-Net in Base 3 — Upper bound on s
There is no (199, 243, 843011)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 87 190324 902292 130460 519578 932937 441217 514931 048085 906044 840993 799885 967452 116469 321781 742205 821134 541428 977188 484861 > 3243 [i]