Best Known (147, 179, s)-Nets in Base 3
(147, 179, 704)-Net over F3 — Constructive and digital
Digital (147, 179, 704)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- digital (124, 156, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 39, 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, 39, 172)-net over F81, using
- digital (7, 23, 16)-net over F3, using
(147, 179, 4052)-Net over F3 — Digital
Digital (147, 179, 4052)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3179, 4052, F3, 32) (dual of [4052, 3873, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3179, 6597, F3, 32) (dual of [6597, 6418, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- 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(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(31) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3179, 6597, F3, 32) (dual of [6597, 6418, 33]-code), using
(147, 179, 740105)-Net in Base 3 — Upper bound on s
There is no (147, 179, 740106)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25 392687 089570 530795 554473 747059 889411 607119 697031 242231 943156 430606 785120 893425 358753 > 3179 [i]