Best Known (119, 119+26, s)-Nets in Base 3
(119, 119+26, 692)-Net over F3 — Constructive and digital
Digital (119, 145, 692)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- 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
- digital (0, 13, 4)-net over F3, using
(119, 119+26, 3551)-Net over F3 — Digital
Digital (119, 145, 3551)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3145, 3551, F3, 26) (dual of [3551, 3406, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3145, 6594, F3, 26) (dual of [6594, 6449, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 31, F3, 3) (dual of [31, 25, 4]-code or 31-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3145, 6594, F3, 26) (dual of [6594, 6449, 27]-code), using
(119, 119+26, 594434)-Net in Base 3 — Upper bound on s
There is no (119, 145, 594435)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1522 597773 188273 569017 381709 446642 839199 913910 163112 805115 371021 160111 > 3145 [i]