Best Known (217−100, 217, s)-Nets in Base 4
(217−100, 217, 130)-Net over F4 — Constructive and digital
Digital (117, 217, 130)-net over F4, using
- t-expansion [i] based on digital (105, 217, 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
(217−100, 217, 200)-Net over F4 — Digital
Digital (117, 217, 200)-net over F4, using
(217−100, 217, 2622)-Net in Base 4 — Upper bound on s
There is no (117, 217, 2623)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 44574 792027 869059 335098 369421 055527 899454 058839 348515 863379 696828 247823 966264 326687 450372 638446 928833 477025 644822 520400 557774 534941 > 4217 [i]