MinT - Best Known (112, 112+34, s)-Nets in Base 4

Best Known (112, 112+34, s)-Nets in Base 4

(112, 112+34, 1036)-Net over F₄ — Constructive and digital

Digital (112, 146, 1036)-net over F₄, using

4² times duplication [i] based on digital (110, 144, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(112, 112+34, 2039)-Net over F₄ — Digital

Digital (112, 146, 2039)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+34, 354356)-Net in Base 4 — Upper bound on s

There is no (112, 146, 354357)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7957 466631 556309 806489 365712 108442 129510 026062 451443 076867 820355 413679 679631 536203 849680 > 4¹⁴⁶ [i]