Best Known (93, 116, s)-Nets in Base 3
(93, 116, 640)-Net over F3 — Constructive and digital
Digital (93, 116, 640)-net over F3, using
- t-expansion [i] based on digital (92, 116, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 29, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 29, 160)-net over F81, using
(93, 116, 1760)-Net over F3 — Digital
Digital (93, 116, 1760)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3116, 1760, F3, 23) (dual of [1760, 1644, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3116, 2223, F3, 23) (dual of [2223, 2107, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(378, 2187, F3, 17) (dual of [2187, 2109, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3116, 2223, F3, 23) (dual of [2223, 2107, 24]-code), using
(93, 116, 238809)-Net in Base 3 — Upper bound on s
There is no (93, 116, 238810)-net in base 3, because
- 1 times m-reduction [i] would yield (93, 115, 238810)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7 395403 359136 839572 620478 332022 552086 609311 874245 431841 > 3115 [i]