Best Known (127, 127+98, s)-Nets in Base 4
(127, 127+98, 130)-Net over F4 — Constructive and digital
Digital (127, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 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
(127, 127+98, 246)-Net over F4 — Digital
Digital (127, 225, 246)-net over F4, using
(127, 127+98, 3664)-Net in Base 4 — Upper bound on s
There is no (127, 225, 3665)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2926 940971 328696 310648 519225 706532 640363 634277 201927 547182 150440 951219 388303 926136 700132 378846 579867 320965 304316 789824 249935 820239 275592 > 4225 [i]