Best Known (102, 102+28, s)-Nets in Base 3
(102, 102+28, 600)-Net over F3 — Constructive and digital
Digital (102, 130, 600)-net over F3, using
- 32 times duplication [i] based on digital (100, 128, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 32, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 32, 150)-net over F81, using
(102, 102+28, 1205)-Net over F3 — Digital
Digital (102, 130, 1205)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3130, 1205, F3, 28) (dual of [1205, 1075, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 2200, F3, 28) (dual of [2200, 2070, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3130, 2200, F3, 28) (dual of [2200, 2070, 29]-code), using
(102, 102+28, 81426)-Net in Base 3 — Upper bound on s
There is no (102, 130, 81427)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 106 115189 960636 033100 786844 439887 914389 602675 391297 184424 210413 > 3130 [i]