Best Known (240−44, 240, s)-Nets in Base 3
(240−44, 240, 1480)-Net over F3 — Constructive and digital
Digital (196, 240, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 60, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(240−44, 240, 4244)-Net over F3 — Digital
Digital (196, 240, 4244)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3240, 4244, F3, 44) (dual of [4244, 4004, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 6592, F3, 44) (dual of [6592, 6352, 45]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3239, 6591, F3, 44) (dual of [6591, 6352, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(39) [i] based on
- linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-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
- construction X applied to Ce(43) ⊂ Ce(39) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3239, 6591, F3, 44) (dual of [6591, 6352, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 6592, F3, 44) (dual of [6592, 6352, 45]-code), using
(240−44, 240, 725720)-Net in Base 3 — Upper bound on s
There is no (196, 240, 725721)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 229308 605851 124038 673707 788440 434849 041146 189065 528701 760198 793983 414406 118852 571761 148945 324133 645259 384130 565769 > 3240 [i]