Best Known (195, 234, s)-Nets in Base 3
(195, 234, 1480)-Net over F3 — Constructive and digital
Digital (195, 234, 1480)-net over F3, using
- t-expansion [i] based on digital (193, 234, 1480)-net over F3, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on digital (193, 236, 1480)-net over F3, using
(195, 234, 8447)-Net over F3 — Digital
Digital (195, 234, 8447)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3234, 8447, F3, 2, 39) (dual of [(8447, 2), 16660, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 9841, F3, 2, 39) (dual of [(9841, 2), 19448, 40]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3234, 19682, F3, 39) (dual of [19682, 19448, 40]-code), using
- 1 times truncation [i] based on linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using
- an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- 1 times truncation [i] based on linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using
- OOA 2-folding [i] based on linear OA(3234, 19682, F3, 39) (dual of [19682, 19448, 40]-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 9841, F3, 2, 39) (dual of [(9841, 2), 19448, 40]-NRT-code), using
(195, 234, 2813169)-Net in Base 3 — Upper bound on s
There is no (195, 234, 2813170)-net in base 3, because
- 1 times m-reduction [i] would yield (195, 233, 2813170)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1476 566907 256102 322513 200775 841761 635727 779510 774639 360621 395545 528955 519435 471940 303070 460742 630199 729120 351985 > 3233 [i]