Best Known (106, 106+34, s)-Nets in Base 3
(106, 106+34, 400)-Net over F3 — Constructive and digital
Digital (106, 140, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 35, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(106, 106+34, 728)-Net over F3 — Digital
Digital (106, 140, 728)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3140, 728, F3, 34) (dual of [728, 588, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3140, 760, F3, 34) (dual of [760, 620, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(310, 31, F3, 5) (dual of [31, 21, 6]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3140, 760, F3, 34) (dual of [760, 620, 35]-code), using
(106, 106+34, 30472)-Net in Base 3 — Upper bound on s
There is no (106, 140, 30473)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 266075 835322 804712 683098 495247 120965 146171 363351 658631 646817 499347 > 3140 [i]