Best Known (61, 61+138, s)-Nets in Base 4
(61, 61+138, 66)-Net over F4 — Constructive and digital
Digital (61, 199, 66)-net over F4, using
- t-expansion [i] based on digital (49, 199, 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
(61, 61+138, 99)-Net over F4 — Digital
Digital (61, 199, 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
(61, 61+138, 427)-Net in Base 4 — Upper bound on s
There is no (61, 199, 428)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 714879 437787 517856 906411 053235 209146 475258 084783 630707 014718 204032 647077 407514 583513 591070 502586 410359 786402 440642 942492 > 4199 [i]