Best Known (56, 224, s)-Nets in Base 4
(56, 224, 66)-Net over F4 — Constructive and digital
Digital (56, 224, 66)-net over F4, using
- t-expansion [i] based on digital (49, 224, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(56, 224, 91)-Net over F4 — Digital
Digital (56, 224, 91)-net over F4, using
- t-expansion [i] based on digital (50, 224, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(56, 224, 235)-Net over F4 — Upper bound on s (digital)
There is no digital (56, 224, 236)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4224, 236, F4, 168) (dual of [236, 12, 169]-code), but
- residual code [i] would yield linear OA(456, 67, F4, 42) (dual of [67, 11, 43]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(456, 67, F4, 42) (dual of [67, 11, 43]-code), but
(56, 224, 365)-Net in Base 4 — Upper bound on s
There is no (56, 224, 366)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 796 257052 715181 823455 940537 797283 441185 843110 935358 811446 148386 073651 536793 416102 585110 865312 484899 203725 762407 060999 980993 171825 201138 > 4224 [i]