MinT - Best Known (111, 111+35, s)-Nets in Base 4

Best Known (111, 111+35, s)-Nets in Base 4

(111, 111+35, 1032)-Net over F₄ — Constructive and digital

Digital (111, 146, 1032)-net over F₄, using

4² times duplication [i] based on digital (109, 144, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(111, 111+35, 1753)-Net over F₄ — Digital

Digital (111, 146, 1753)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+35, 326605)-Net in Base 4 — Upper bound on s

There is no (111, 146, 326606)-net in base 4, because

1 times m-reduction [i] would yield (111, 145, 326606)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 355694 078752 161148 877509 761244 772378 545456 439881 046155 553175 531264 014335 702561 851988 > 4¹⁴⁵ [i]