Best Known (255−192, 255, s)-Nets in Base 4
(255−192, 255, 66)-Net over F4 — Constructive and digital
Digital (63, 255, 66)-net over F4, using
- t-expansion [i] based on digital (49, 255, 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
(255−192, 255, 99)-Net over F4 — Digital
Digital (63, 255, 99)-net over F4, using
- t-expansion [i] based on digital (61, 255, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(255−192, 255, 260)-Net over F4 — Upper bound on s (digital)
There is no digital (63, 255, 261)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4255, 261, F4, 192) (dual of [261, 6, 193]-code), but
- construction Y1 [i] would yield
- linear OA(4254, 258, F4, 192) (dual of [258, 4, 193]-code), but
- linear OA(46, 261, F4, 3) (dual of [261, 255, 4]-code or 261-cap in PG(5,4)), but
- construction Y1 [i] would yield
(255−192, 255, 408)-Net in Base 4 — Upper bound on s
There is no (63, 255, 409)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3504 466943 141357 706431 054402 816194 784013 225294 235578 882834 904033 529328 212624 010168 105804 698737 749838 099440 758492 227001 367650 461622 613600 337968 872485 293676 > 4255 [i]