MinT - Best Known (143, 143+46, s)-Nets in Base 4

Best Known (143, 143+46, s)-Nets in Base 4

(143, 143+46, 1032)-Net over F₄ — Constructive and digital

Digital (143, 189, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (142, 188, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 47, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(143, 143+46, 2007)-Net over F₄ — Digital

Digital (143, 189, 2007)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+46, 278399)-Net in Base 4 — Upper bound on s

There is no (143, 189, 278400)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615681 986437 718175 517620 613128 262918 914495 180787 426509 558789 914526 245613 469084 697846 070155 404056 547138 288017 672121 > 4¹⁸⁹ [i]