Best Known (117, 117+36, s)-Nets in Base 3
(117, 117+36, 464)-Net over F3 — Constructive and digital
Digital (117, 153, 464)-net over F3, using
- 31 times duplication [i] based on digital (116, 152, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 38, 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, 38, 116)-net over F81, using
(117, 117+36, 865)-Net over F3 — Digital
Digital (117, 153, 865)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3153, 865, F3, 36) (dual of [865, 712, 37]-code), using
- 125 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0) [i] based on linear OA(3141, 728, F3, 36) (dual of [728, 587, 37]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 125 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0) [i] based on linear OA(3141, 728, F3, 36) (dual of [728, 587, 37]-code), using
(117, 117+36, 42899)-Net in Base 3 — Upper bound on s
There is no (117, 153, 42900)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9 991204 365034 073751 490170 889066 104582 186396 778956 203740 206992 529569 394841 > 3153 [i]