Best Known (125, 125+117, s)-Nets in Base 4
(125, 125+117, 130)-Net over F4 — Constructive and digital
Digital (125, 242, 130)-net over F4, using
- t-expansion [i] based on digital (105, 242, 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
(125, 125+117, 189)-Net over F4 — Digital
Digital (125, 242, 189)-net over F4, using
(125, 125+117, 2328)-Net in Base 4 — Upper bound on s
There is no (125, 242, 2329)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 241, 2329)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 762277 559691 087398 548408 831766 909059 466279 265464 985408 146105 073772 038102 329800 224986 738555 039242 011377 388869 686257 928161 359112 362697 309537 506560 > 4241 [i]