Best Known (62, 246, s)-Nets in Base 4
(62, 246, 66)-Net over F4 — Constructive and digital
Digital (62, 246, 66)-net over F4, using
- t-expansion [i] based on digital (49, 246, 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
(62, 246, 99)-Net over F4 — Digital
Digital (62, 246, 99)-net over F4, using
- t-expansion [i] based on digital (61, 246, 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
(62, 246, 259)-Net over F4 — Upper bound on s (digital)
There is no digital (62, 246, 260)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4246, 260, F4, 184) (dual of [260, 14, 185]-code), but
- residual code [i] would yield linear OA(462, 75, F4, 46) (dual of [75, 13, 47]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(462, 75, F4, 46) (dual of [75, 13, 47]-code), but
(62, 246, 403)-Net in Base 4 — Upper bound on s
There is no (62, 246, 404)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13475 483952 346046 584840 481041 492032 547580 787745 824318 879400 470865 961055 901608 474213 839585 268705 066449 595553 449763 615182 613181 850568 274214 910543 461280 > 4246 [i]