Best Known (100, 100+28, s)-Nets in Base 3
(100, 100+28, 600)-Net over F3 — Constructive and digital
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
(100, 100+28, 1106)-Net over F3 — Digital
Digital (100, 128, 1106)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3128, 1106, F3, 28) (dual of [1106, 978, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3128, 2195, F3, 28) (dual of [2195, 2067, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(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(31, 8, F3, 1) (dual of [8, 7, 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
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3128, 2195, F3, 28) (dual of [2195, 2067, 29]-code), using
(100, 100+28, 69597)-Net in Base 3 — Upper bound on s
There is no (100, 128, 69598)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 790857 236022 903991 812489 605365 757563 713990 064830 026503 363189 > 3128 [i]