Best Known (239−42, 239, s)-Nets in Base 3
(239−42, 239, 1480)-Net over F3 — Constructive and digital
Digital (197, 239, 1480)-net over F3, using
- t-expansion [i] based on digital (196, 239, 1480)-net over F3, using
- 1 times m-reduction [i] based on 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
- trace code for nets [i] based on digital (16, 60, 370)-net over F81, using
- 1 times m-reduction [i] based on digital (196, 240, 1480)-net over F3, using
(239−42, 239, 5402)-Net over F3 — Digital
Digital (197, 239, 5402)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3239, 5402, F3, 42) (dual of [5402, 5163, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3239, 6614, F3, 42) (dual of [6614, 6375, 43]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [i] based on
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(314, 53, F3, 6) (dual of [53, 39, 7]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [i] based on
- discarding factors / shortening the dual code based on linear OA(3239, 6614, F3, 42) (dual of [6614, 6375, 43]-code), using
(239−42, 239, 1168286)-Net in Base 3 — Upper bound on s
There is no (197, 239, 1168287)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 076431 639118 659999 433618 400026 122015 905062 280674 046569 919909 167382 946722 255910 157421 239230 793320 546273 248229 796375 > 3239 [i]