MinT - Best Known (142−34, 142, s)-Nets in Base 4

Best Known (142−34, 142, s)-Nets in Base 4

(142−34, 142, 1032)-Net over F₄ — Constructive and digital

Digital (108, 142, 1032)-net over F₄, using

4² times duplication [i] based on digital (106, 140, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 35, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(142−34, 142, 1726)-Net over F₄ — Digital

Digital (108, 142, 1726)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−34, 142, 255724)-Net in Base 4 — Upper bound on s

There is no (108, 142, 255725)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 083616 980264 478076 958303 331676 595088 096352 356678 139272 922245 178494 278971 320830 234256 > 4¹⁴² [i]