Best Known (202, 248, s)-Nets in Base 3
(202, 248, 1480)-Net over F3 — Constructive and digital
Digital (202, 248, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 62, 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
(202, 248, 4072)-Net over F3 — Digital
Digital (202, 248, 4072)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3248, 4072, F3, 46) (dual of [4072, 3824, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3248, 6588, F3, 46) (dual of [6588, 6340, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(40) [i] based on
- linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
- an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- construction X applied to Ce(45) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(3248, 6588, F3, 46) (dual of [6588, 6340, 47]-code), using
(202, 248, 657692)-Net in Base 3 — Upper bound on s
There is no (202, 248, 657693)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21187 086130 093863 176501 766493 972572 308039 569770 802329 106236 450972 561533 217187 238677 421634 809211 869168 871101 870399 104123 > 3248 [i]