Best Known (107, 107+26, s)-Nets in Base 3
(107, 107+26, 688)-Net over F3 — Constructive and digital
Digital (107, 133, 688)-net over F3, using
- 31 times duplication [i] based on digital (106, 132, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 33, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 33, 172)-net over F81, using
(107, 107+26, 2041)-Net over F3 — Digital
Digital (107, 133, 2041)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3133, 2041, F3, 26) (dual of [2041, 1908, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3133, 2201, F3, 26) (dual of [2201, 2068, 27]-code), using
- (u, u+v)-construction [i] based on
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(3133, 2201, F3, 26) (dual of [2201, 2068, 27]-code), using
(107, 107+26, 215609)-Net in Base 3 — Upper bound on s
There is no (107, 133, 215610)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2865 052743 759499 754500 122508 832359 515283 256157 489903 408220 741501 > 3133 [i]