Best Known (67, 67+76, s)-Nets in Base 4
(67, 67+76, 66)-Net over F4 — Constructive and digital
Digital (67, 143, 66)-net over F4, using
- t-expansion [i] based on digital (49, 143, 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
(67, 67+76, 99)-Net over F4 — Digital
Digital (67, 143, 99)-net over F4, using
- t-expansion [i] based on digital (61, 143, 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
(67, 67+76, 892)-Net in Base 4 — Upper bound on s
There is no (67, 143, 893)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 126 917553 630149 942117 305246 513394 236388 347131 150516 150200 993395 922399 655005 294753 443780 > 4143 [i]