MinT - Best Known (114−26, 114, s)-Nets in Base 4

Best Known (114−26, 114, s)-Nets in Base 4

(114−26, 114, 1036)-Net over F₄ — Constructive and digital

Digital (88, 114, 1036)-net over F₄, using

4² times duplication [i] based on digital (86, 112, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 28, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(114−26, 114, 1900)-Net over F₄ — Digital

Digital (88, 114, 1900)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−26, 114, 359646)-Net in Base 4 — Upper bound on s

There is no (88, 114, 359647)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 431 371999 802797 219456 492893 376176 759289 901328 838425 217775 370232 670338 > 4¹¹⁴ [i]