Best Known (101−22, 101, s)-Nets in Base 3
(101−22, 101, 464)-Net over F3 — Constructive and digital
Digital (79, 101, 464)-net over F3, using
- 31 times duplication [i] based on digital (78, 100, 464)-net over F3, using
- t-expansion [i] based on digital (77, 100, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 25, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 25, 116)-net over F81, using
- t-expansion [i] based on digital (77, 100, 464)-net over F3, using
(101−22, 101, 1098)-Net over F3 — Digital
Digital (79, 101, 1098)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3101, 1098, F3, 2, 22) (dual of [(1098, 2), 2095, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3101, 2196, F3, 22) (dual of [2196, 2095, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3101, 2197, F3, 22) (dual of [2197, 2096, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(392, 2187, F3, 20) (dual of [2187, 2095, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(385, 2187, F3, 19) (dual of [2187, 2102, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3101, 2197, F3, 22) (dual of [2197, 2096, 23]-code), using
- OOA 2-folding [i] based on linear OA(3101, 2196, F3, 22) (dual of [2196, 2095, 23]-code), using
(101−22, 101, 58985)-Net in Base 3 — Upper bound on s
There is no (79, 101, 58986)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 546190 123756 610610 200697 003063 128804 271980 379361 > 3101 [i]