MinT - Best Known (89, 89+28, s)-Nets in Base 4

Best Known (89, 89+28, s)-Nets in Base 4

(89, 89+28, 1032)-Net over F₄ — Constructive and digital

Digital (89, 117, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (88, 116, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(89, 89+28, 1493)-Net over F₄ — Digital

Digital (89, 117, 1493)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+28, 216678)-Net in Base 4 — Upper bound on s

There is no (89, 117, 216679)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27608 197834 057714 057676 393567 582170 482151 155620 307956 587451 741970 249724 > 4¹¹⁷ [i]