MinT - Best Known (242−58, 242, s)-Nets in Base 4

Best Known (242−58, 242, s)-Nets in Base 4

(242−58, 242, 1036)-Net over F₄ — Constructive and digital

Digital (184, 242, 1036)-net over F₄, using

4² times duplication [i] based on digital (182, 240, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 60, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(242−58, 242, 2677)-Net over F₄ — Digital

Digital (184, 242, 2677)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−58, 242, 411208)-Net in Base 4 — Upper bound on s

There is no (184, 242, 411209)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 948002 354113 147472 291554 645676 637215 479720 818992 114801 582528 003801 023962 479134 394091 363590 784916 080587 606548 727300 715690 857546 207041 384062 801792 > 4²⁴² [i]