Best Known (121, 121+97, s)-Nets in Base 4
(121, 121+97, 130)-Net over F4 — Constructive and digital
Digital (121, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(121, 121+97, 224)-Net over F4 — Digital
Digital (121, 218, 224)-net over F4, using
(121, 121+97, 3252)-Net in Base 4 — Upper bound on s
There is no (121, 218, 3253)-net in base 4, because
- 1 times m-reduction [i] would yield (121, 217, 3253)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 44463 923205 624437 890254 736024 940012 747848 328524 326457 610508 981475 098366 701646 665979 619751 684966 296709 949095 032402 109297 472999 629545 > 4217 [i]