Best Known (194, 236, s)-Nets in Base 3
(194, 236, 1480)-Net over F3 — Constructive and digital
Digital (194, 236, 1480)-net over F3, using
- t-expansion [i] based on digital (193, 236, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 59, 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, 59, 370)-net over F81, using
(194, 236, 4972)-Net over F3 — Digital
Digital (194, 236, 4972)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 4972, F3, 42) (dual of [4972, 4736, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 6605, F3, 42) (dual of [6605, 6369, 43]-code), using
- strength reduction [i] based on linear OA(3236, 6605, F3, 43) (dual of [6605, 6369, 44]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- strength reduction [i] based on linear OA(3236, 6605, F3, 43) (dual of [6605, 6369, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 6605, F3, 42) (dual of [6605, 6369, 43]-code), using
(194, 236, 998591)-Net in Base 3 — Upper bound on s
There is no (194, 236, 998592)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 39867 862636 099485 446483 146902 493212 508399 443535 460473 901791 411213 943064 798432 688065 897486 294870 298659 729637 212545 > 3236 [i]